Unit 8: Comparing Solar Systems

This material was developed by the Friends of the Dominion Astrophysical Observatory with the assistance of a Natural Science and Engineering Research Council PromoScience grant and the NRC. It is a part of a larger project to present grade-appropriate material that matches 2020 curriculum requirements to help students understand planets, with a focus on exoplanets. This material is aimed at BC Grade 6 students. French versions are available.

Instructions for teachers ● For questions and to give feedback contact: Calvin Schmidt [email protected], ​ ● All units build towards the Big Idea in the curriculum showing our solar system in the context of the Milky Way and the Universe, and provide background for understanding exoplanets. ● Look for Ideas for extending this section, Resources, and Review and discussion ​ ​ ​ ​ ​ questions at the end of each topic in this Unit. These should give more background on ​ each subject and spark further classroom ideas. We would be happy to help you ​ expand on each topic and develop your own ideas for your students. Contact us at ​ the [email protected]. ​ ​

Instructions for students ● If there are parts of this unit that you find confusing, please contact us at [email protected] for help. ​ ● We recommend you do a few sections at a time. We have provided links to learn more about each topic. ● You don’t have to do the sections in order, but we recommend that. Do sections you find interesting first and come back and do more at another time. ● It is helpful to try the activities rather than just read them. ● Explore the “Ideas for extending this section” and “Resources” sections at the end of each topic in this Unit - they aren’t just for teachers!

Learning Objectives ● The BC curriculum requires students to learn: ○ about the “Components of our solar system”: studying the orbits and scale of our solar system helps meet this requirement. ○ “[How the] exploration of extreme environments on Earth and in space changed in the last decade?” and also “Canada’s contribution to exploring extreme environments” (in the context of planets)

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● Students will not be limited to talking about planets in our solar system and will learn about planets around other stars in order to expand the range of environments and see our solar system as one of many.

Learning Outcomes ● Students will: ○ understand the scale of our solar system and how exoplanet orbits compare ○ understand how orbits can affect the environment, sometimes leading to extreme environments on other worlds. ○ understand two geometric shapes, ellipses and hyperbolas, with an emphasis on ellipses ○ understand how our understanding of our solar system’s configuration changed over time

Materials and tools needed for the activities ● Activity 1 - Stellarium Installed ● Activity 2 ● Activity 3 - This link : https://www.exploratorium.edu/ronh/age/ ​

Time Required ● Lesson time - 90 minutes ● Activity time ○ Activities 1 and 2: 15 minutes each ○ Activity 3: 5 to 10 minutes

Contents The activities are marked in yellow. ​

● Families of worlds ● Do planets really "wander"? ○ Activity 1: Retrograde Motion ● Orbit shapes ○ Activity 2: Making ellipses ● Orbit Sizes ● How long is a year on different planets? ○ Activity 3: How old are you by different planet years? ● Different kinds of solar systems ● The Goldilocks zone

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F amilies of worlds

If you watch science fiction like Star Wars or Star Trek you take for granted that there are planets going around other stars. But we’ve only learned that there really are other solar systems in the last thirty years, which is within the lifetime of most of the parents of grade 6 students. As we’ve mentioned, 3,176 solar systems have been found at the time of writing in August 2020, and more will soon be found. Are these families of worlds, each born together, like ours with small rocky planets close to their star and gas giant planets further out? How are these other solar systems different from ours, and how are they the same? If our solar system is unusual, do we know why?

You’ll start by learning a little about how astronomers figured out that we are living in a solar system, then you’ll learn about orbits, and then compare known solar systems, many of which are quite different from our own.

D o planets really “wander”?

In the last unit we talked about how the word “planet” is the Greek word for “wanderer”, and how they were called that because they looked like stars that moved around. Think for a minute about what “wander” really means. If you are wandering, are you following a plan, or a specific route? When people wander they don’t follow a set path, and instead make it up as they go along, seldom going the same route twice. That’s not what planets do.

The Greeks and others who watched carefully noticed that the planets move in ways that have special shapes and paths, and those paths are quite predictable and usually repeat. It’s the opposite of wandering.

Most ancient peoples thought the Earth was at rest: it did not give the impression of wandering or having any sort of motion at all. There was no effect like a wind that blew from one direction constantly, like they expected for a moving Earth. That’s what they experienced when running fast or riding a horse: air rushes past your head.

The stars and planets, as we discussed in Unit 1: Stars and Distances, appeared to be of the same distance. The stars seemed to turn together, but people noticed that the Sun and Moon seemed to move at a slightly different rate than the stars but did not collide even though they passed each other in the sky once a month. To explain this, a Greek academic named Anaximander who lived around 2,600 years ago, argued that they must be something like spinning Chariot wheels, one inside the other, with us at the centre. He suggested these wheels turned at different rates. Anaximander thought that the light of the Moon and Sun came from a little window showing the fire on the inside of each wheel. Even before we could prove that the Sun and Moon were at different distances from us, which Hipparchus did 500 years later, the

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idea that they were at different distances was suggested by Anaximander to explain sky motions.

Later Greeks imagined that these wheels were instead thin transparent rings or spheres, one inside the other, made out of something similar to the clear crystal, a material they knew about. To explain the planets, which moved more slowly than the Moon and Sun, they put them further out from the Earth, which they put at the centre. If you look at a cross-section of this, as you can see in Figure 1, the circular paths of the planets look a bit like orbits, but they didn’t imagine that the planets were even worlds, let alone zipping through empty space. Notice that the stars are near the outside, with the Earth in the middle.

Figure 1: Celestial Spheres (Engraving from Peter Apian's Cosmographia, 1524) ​

This was a good start, but it didn’t explain how things moved in the sky precisely. While it seemed to explain some things about the speeds at which things moved across the sky, it ran into problems with trying to explain the details of motions of the planets, especially Mercury and Venus, which we now know are closer to the Sun than us. Mars would also, for example,

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change directions in where it moved among the stars every two years, doing a loop over a period of a couple of months.

A Greek named Philolaus who lived about 2,400 years ago tried to solve the problem by ​ suggesting that there was a central fire surrounded by the planets and our Sun, Moon, and Earth orbited it. In this complicated idea, Philolaus imagined that we couldn’t see the central fire because another Earth blocked our view of it! Of course, he had no evidence for another Earth or a central fire that was always invisible to us. On the other hand, it was the first time someone suggested that the spinning of the Earth gave us day and night, and that the Earth orbited something. It still didn’t fully explain the motions of the planets, however.

A Greek astronomer who lived about 100 years later, Aristarchus, built on Philolaus’ ideas and made the Sun the “central fire”, and also put each planet in its correct order from the Sun. This was the first “heliocentric” system, “helio” being the Greek word for “Sun”, and “centric” meaning “centred”. He realized that this would explain the motions of each celestial object much better, and he said that the Earth moved around the Sun, which was a new idea. Aristarchus, who could prove the relative distances of the Moon and Sun, realized that the solar system must be large, and reasoned that the stars were other suns seen at a great distance.

Aristarchus was correct, but most people were not convinced. Seleucus, who lived about 100 years later, is thought to have found more proof by using Aristarchus’ theory to predict the motions of planets with greater accuracy. But most people supported the idea that the Earth was at the centre and crystalline spheres revolved around us, an idea promoted by Ptolemy and by the influential philosopher Aristotle. Aristotle’s complicated system used up to 55 nested crystal spheres. This was the “Geocentric” system, “Geo” meaning “Earth”.

Aristotle and Ptolemy’s idea, which was also supported by church authorities because it put Earth at the centre, was popular for another 1,800 years in both Europe and Arabic and Persian regions, even though the idea didn’t fully explain why planets moved like they did, despite repeated efforts by astronomers in these areas. Nicolaus Copernicus revived Aristarchus’ idea of a Sun-centred solar system in 1543 at a time when questioning such things became possible in Europe.

While this sun-centred idea where planets moved in circular orbits predicted the motions of the planets better than the Earth-centred one, it didn’t explain everything people were seeing. Johannes Kepler thought it was an issue of getting the spacing of the “celestial spheres” right, but he couldn’t make it work. He needed to explain the “retrograde loop” that Mars does in the sky better, for example.

When Kepler started using precise positions of the motions of the planets that he got from his friend Tycho Brahe he was forced to abandon the idea that the planets were stuck on spheres, and said instead that they moved in elliptical paths. We show an exaggerated example of this

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idea in Figure 2. Planet orbits in our solar system are not this exaggerated, as you’ll see later in this unit.

To explain Tycho’s observations, he also showed that the planets moved faster when they were closest to the Sun and slowest when they were furthest away. He was unhappy that the planets didn’t move in perfect circles, but he accepted the evidence, a sign that he was an excellent scientist who valued the truth above his preference. He did not live long enough to know why they moved like this.

Figure 2: A planet orbiting the Sun in an ellipse (we have exaggerated the ellipse to show that it is not a circle)

Galileo, who lived around the time of Kepler and Brahe, explained that objects that were in motion would tend to stay in motion unless a force was applied to make them stop. This is the modern concept of inertia, and that explained why the planets would continue to move along their orbits if they weren’t attached to anything like a spinning crystal sphere. It also explained why we don’t feel wind as the Earth spins: the air turns with us.

Sir Isaac Newton gave the rest of the answer about planetary motion. Newton, who was born about 25 years later, explained that gravity created a mutual pull between the Sun and a planet, and the Earth and its Moon. The mathematics of his theory of gravity showed why planets move fastest when they were closest to the Sun.

By noticing that the Moon, Sun, and planets don’t wander aimlessly in the sky, but instead move in very specific ways, and trying to explain those movements in great detail, astronomers were able to bring us to our modern understanding of worlds that move through space under the influence of gravity. They showed that these objects don’t need to be attached to anything, and that the planets would keep moving along their orbits unless a force was applied to change the

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motion. Newton’s law of universal gravitation even allowed us to discover the outermost planet of the solar system, Neptune!

During the 19th century, astronomers observed irregularities in the orbit of Uranus; it wasn’t moving exactly like we expected it to be. Some astronomers were starting to think that another planet could be located further away, and affecting the orbit of Uranus. The British astronomer John Couch Adams and the French astronomer Urbain Le Verrier each started their own study of Uranus’ orbit (in 1843 and 1845 respectively), trying to calculate the position of this hypothesised planet. Neither of them knew about the other’s work.

On September 23rd 1846, the german astronomer Johann Gottfried Galle used his telescope along with Le Verrier’s calculations to observe the area of the sky where he predicted this new planet would be located, where he found an unknown star. On the next night, Galle saw that this new star had moved relatively to the other background stars, confirming that it was a planet, which we now know as Neptune.

Figure 3: Timeline of the astronomers mentioned in the text.

There were many astronomers and philosophers who tried to understand our Solar System, and how the planets moved in the sky. By 1846, scientists had a fairly good grasp of it, although more celestial discoveries would be made. Figure 3 shows some of the people mentioned.

A ctivity One - Observing the retrograde motion of Mars In this activity, we will see how the rather simple elliptical orbits of some planets can cause unusual patterns of motion in the sky. First, we will be using Stellarium to observe Mars’ motion from Earth.

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● Open Stellarium, and as usual minimize light pollution for a better view. If you don’t remember how to do this, see the 3rd activity of Unit 3. Don’t deactivate solar system objects since we’ll want to observe Mars’ trajectory. ● Set the date to the 11th of November 2011, anytime at night. On this particular day, Mars will be very close to the star Regulus in the Leo constellation. ● Use the bottom toolbar to deactivate the ground and cardinal points and activate constellations if they weren’t already visible. ● Find Mars using the search bar (F3) and click on it once to select it. ● In the SSO tab of the sky and viewing options, tick the “show orbits (only for selected object)” and the “show trails” boxes. ● The red line that appears will show the orbit of Mars viewed from the night sky. You’ll see that it looks circular if you zoom out enough, which is why early astronomers thought planets might be orbiting in circles. ● Now zoom back on the Leo constellation to see it clearly, and either double click on Regulus, or switch to an equatorial mount; we want to keep the sky fixed here. ● Open the date and time window, move it to the side of your screen so it doesn’t bother the view. Now increase the date in increments of one day and look at the trail that Mars is leaving. By May 2012, you’ll see that it has made a loop! This is called retrograde motion.

But if planets orbit the Sun in ellipses, what causes this unusual motion ? Let’s look into it with more details.

● Follow this link to open an excellent simulation of retrograde motion ​ ● In the center of the simulation, you’ll see Venus, Earth and Mars. ● You can choose to look from any of these planets, and to look towards any of the other two. The outer band of the simulation (the one that has stars in it) shows you the view when looking at the sky towards the planet you chose to observe. ● If you look at how the planets are orbiting the Sun, you should easily notice that the Earth completes its orbits much faster than Mars. Mars’ orbital period is 687 days, which is close to twice as long as Earth’s 365 days. ● Make sure to adjust the view controls so you’re looking at Mars and from Earth. Activate “show trace” (and “use directional coloring” if you want to). And take a good look at the view of Mars from Earth. ● You’ll notice that whenever the Earth starts catching up to Mars and overtakes it, it looks like Mars decides to move backwards for a moment then goes back to following its usual path. This is the moment when it traces a loop in the sky. ● Retrograde motion is similar to what happens when a passenger is looking through the car window while the driver is overtaking another car on the highway. For a moment it looks like the other car is going backwards, when really you’re just moving faster.

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● If you want, you can use the simulation to try to observe retrograde motion from another planet, or change the planet orbits and see how that affects the apparent motion. Have fun!

Figure 4: The retrograde path of Mars as viewed from Earth (from Stellarium)

Ideas for extending this section: ● Try wandering in different ways. One way is to start walking and make decisions along the way about what interests you, or simply what you prefer in that moment. Another way is to wander in a random way. How do the two paths differ? If you want to see truly random wandering, look up “Brownian Motion”.

Resources and references: ● Brownian motion (Minute Labs) ​ ● The Discovery of Neptune (EarthSky) ​ ● Geocentric Model (Wikipedia) ​ ● Heliocentrism (Wikipedia) ​

Review and discussion questions: ● Discuss why the Greek astronomers were bothered when their ideas didn’t match what was in the sky, but people in Europe and elsewhere didn’t challenge the wrong idea for 1,800 years.

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O rbit Shapes

The simplest type of orbit to describe is a circle. This is an orbit with a constant radius: all points on it are the same distance from the centre. Interestingly, the first orbits described that have nothing to do with “celestial spheres” are ellipses. Orbits in our solar system are all ellipses: we don’t know of any orbits that are perfect circles. To get a better understanding of ellipses, try Activity Two before moving on.

A ctivity Two - Making ellipses

R equired tools and materials: ● Two sheets of paper, a pencil, and a ruler ● Nails, pins or tacks ● A piece of string (40cm long or more) ● Some cardboard ● Optional: pencil crayons

Ellipses look a bit like a circle that has been squished. Eggs, grapes and footballs are common household objects whose shape resembles that of an ellipse (but not perfectly). Let’s try and draw an ellipse!

First take a piece of cardboard and place a sheet of paper on top of it. Take 2 pins (or equivalent objects) and place them 16 cm apart around the center of your paper. Then take your piece of string and tie a knot between its ends to create a loop, then tie it around the pins. With your pencil, pull on the string until it is tightly stretched (forming a triangle with the pins) and then move it in a large arc. You’ll draw out your ellipse! Just make sure to keep the string taut at all times.

Here is a youtube video showing this process: Ellipse - Pin & String Method ​

As you could see in the video, if you progressively move your pins closer to one another, your ellipse will get wider and wider. Try it yourself by moving the pins closer by 2cm at a time. The moment your pins are on the same point, you will realize that you’re drawing a circle! That’s because your pins are placed on what we call the focal points (or foci) of your ellipse, and a circle is actually just a special type of ellipse where both foci are placed at the same spot.

All the ellipses you drew should look quite different from one another. The first ones should look quite “squished”, and the ones you drew after moving the pins closer together looked more and more like a circle. There is a number called the “eccentricity” of an ellipse which measures how much an ellipse looks like a circle. This number is always between 0 and 1 (but never 1 if it’s an ellipse). The closer the eccentricity is to zero, the more the ellipse will look like a circle. A circle

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is an ellipse with zero eccentricity. By the same logic, the closer the eccentricity is to one, the less the ellipse looks like a circle; it will be a lot wider than it is tall (“squished” if you prefer).

Let’s look a bit more into the different properties and measurable dimensions of an ellipse.

Take another sheet of paper and draw another ellipse using the previous method. Make sure the pins are far enough apart because you’ll want an eccentric ellipse to best illustrate these. We will be marking a few special points on the ellipse, so feel free to use pencil crayons for those markings if it helps you distinguish them. ● Once you’ve drawn your ellipse, remove the pins and mark their position by an F (for focus/focal point). ● Next, take a ruler and draw a line going through both foci and stop it when it touches the edge of the ellipse. This line you drew is called the “major axis”, it’s the longest dimension of the ellipse. ● The center point of the major axis is also the center of the ellipse, mark this point by the letter O (for origin). ● The point where the major axis touches the ellipse is called a vertex. There are two vertices, mark them both by the letter V. ● Draw a perpendicular line to the major axis which passes through the center (point O), and extend it until you touch the edges of the ellipse again. This line is called the minor axis as it is smaller in length than the major axis. ● The minor axis touches the ellipse on two points, which are called the co-vertices. Mark them by the letter C. ● Once you’re done drawing, it should look like the Figure 5 below.

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Figure 5: An ellipse marked with the major axis (red) and minor axis (blue). The origin, foci, vertices, and co-vertices are marked as well.

As we’ve said previously, planets don’t orbit their Sun in perfect circles. Instead, a planet traces an ellipse, and its host star is located on one of the ellipse’s foci. Choose one of the focus points in your drawing to be the location of the Sun and draw a yellow circle on it. The planet’s path is described by the ellipse, you can add some arrows to show which direction your planet is orbiting.

Eccentric Orbits

There are two special points in the orbit of a planet, and those are the vertices of the ellipse. The vertex that is closest to the star is called “perihelion”, and the one that is farthest from it is called “aphelion”

When a planet is at aphelion, it will receive less light from its star than at perihelion. However, the difference between the light received at aphelion and perihelion really depends on the eccentricity of the orbit, as that’s what will determine how elongated the ellipse will be. And the eccentricity of a planet’s orbit can vary quite a lot.

Let’s start by looking at the eccentricities of our solar system’s planets.

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Table 1: The orbit eccentricities of our solar system’s planets (from smallest to biggest) Planet Eccentricity

Venus 0.0068

Neptune 0.0086

Earth 0.0167

Uranus 0.0472

Jupiter 0.0484

Saturn 0.0542

Mars 0.0934

Mercury 0.2056

Pluto, a dwarf planet, has an even greater orbit eccentricity of 0.2488, even more than Mercury, and Eris, another dwarf planet, has an eccentricity of 0.44. The dwarf planets that are far flung out in the Solar System tend to have higher eccentricities.

Of the planets, Mercury has the most eccentricity, and Venus has the least. Venus is more like a circle. If we make their orbits look like they are the same size, we notice that one orbit appears more ‘squished’ than the other. You can bet that Mercury, with the high eccentricity is the one that is the most ‘squished’ one. Figure 6 shows this, where Venus is the pink orbit, and Mercury is the green orbit. The eccentricity of Mercury means that it gets closer to the Sun at one end of the orbit, and farther from the Sun at the opposite end. Notice that if the orbits really were the same size, Mercury would cross the path of Venus.

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Figure 6: Venus’ ellipse (in pink) compared to Mercury’s (green). The orbits are different sizes but we’ve made them the same size here just to compare the eccentricity.

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Figure 7: Similar to Figure 6, but with the planets orbiting the Sun. Mercury, with the most eccentric orbit, gets closer to, and farther from the Sun, than Venus.

Earth’s orbit varies between 0.0034 - even less eccentricity than Venus’ right now - to 0.058, more than Saturn’s right now, but it takes about 100,000 years for it to go from one extreme to another. It is currently getting more circular. Which extreme are we closest to right now? As you can see, in Figure 8, even at its most eccentric, our orbit looks almost like a circle.

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Figure 8: Can you see the difference between Earth’s orbit extremes? The blue orbit is more eccentric than the more circular red orbit.

The planets in our solar system, as you can see, have orbits that are nearly circular. Before astronomers found exoplanets they thought that their orbits should be nearly circular like ours. While many are, the most eccentric exoplanet orbit found, for planet HD 20782, is 0.95! Let’s ​ have a look at that in figure 9. This is similar to the eccentricity of a well-known comet, Halley’s Comet, the first comet whose orbit was accurately determined. In Unit 6, we briefly mentioned that comets orbit the Sun far away, then move in really close. They are on highly eccentric orbits. We’ll talk more about comets in coming units, but for now you can think of a comet as a mountain-sized mix of dust and ices.

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Figure 9: This is the orbit of HD 20782, the exoplanet with the most eccentric planet orbit known.

One-direction orbits

Sometimes, orbits cross. In Kepler’s time 400 years ago astronomers thought that each orbit was inside another. We now know that isn’t always the case. The dwarf planet Pluto is known to have an orbit that comes both closer to and farther from the Sun than Neptune, and the comet just mentioned, Halley’s comet, crosses the orbits of Venus and Neptune on its journey. Asteroids can also cross the orbits of planets. This can lead to collisions, but of course the timing has to be just right so that both planet and asteroid are in the same place at the same time. None of the eight major planets in our solar system have orbits that cross each other, but this may not be true for exoplanets.

Planets move like they are on a one-way street: they all orbit in the same direction. When we discussed how planets formed in Unit 6 - The Birth of Stars and Planets, we saw how planets formed out of spinning protoplanetary disks.

This is also why planets orbit in the same direction, which is also the same direction that our Sun spins in. Exoplanets have shown us that this is once again not the case everywhere. For ​ example, planets have been found to orbit a star in the opposite direction to which the star spins. Still, all the planets in that case still orbit in the same direction.

Tilted orbits

The protoplanetary nebula was flat, so we expect the orbits to be nearly flat. Pluto is another exception here, as it has an orbit tilted by a large amount compared to the Earth’s amount.

In our solar system, the giant planets like Jupiter and Saturn have orbits that are not tilted much. Figure 10 shows the angles of the planets, and Table 2 displays the angle in degrees. ​

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But with exoplanets they have found giant planets with orbits tilted by a large amount compared to one another in systems where there is more than one planet. These giant planets are also in orbits that have large eccentricities. Only a few multiple planet systems have had the tilt of their orbits measured, however. One system, Upsilon Andromedae, has a difference of about 30 degrees between two planet orbits, even more than the tilt of Pluto’s orbit. A comparison of Upsilon Andromedae and the Solar System can be seen in Figures 10 and 11. This was surprising to astronomers as they thought the orbits would be similar in tilt, like they are in our solar system, because the planets form from a disk.

Figure 10: The angles at which some worlds orbit their star.

Table 2: The tilt of the orbits of our solar system’s planets and dwarf planets relative to Earth, plus exoplanet Upsilon Andromedae d for comparison

Planet / Dwarf Planet Orbital tilt (in degrees)

Earth 0

Uranus 0.77

Jupiter 1.33

Neptune 1.77

Mars 1.85

Saturn 2.49

Venus 3.39

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Mercury 7.01

Pluto 17

Upsilon Andromedae d 30

Figure 11: The planetary system Upsilon Andromedae, compared to ours. Note that planet d is not in the same plane as planet c. (courtesy ESA/Hubble Space Telescope)

A one-time-only orbit

We think of orbits as a planet going around on a path that repeats (even if that shape changes with time), but there is a type of “orbit” where the object only follows it once. In this type of orbit,

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the object only goes by the Sun once before leaving the solar system. No planet has been found to follow this type of path but there have been two smaller objects that have been spotted to do this in our solar system, they were called Oumuamua and Borisov and were discovered in 2017 and 2019 respectively. They came from outside of the solar system. Figure 12 shows ‘Oumuamua and its path through the Solar System. The shape of this orbit, a hyperbola, can be found in many places around us, including the curve in the body of a guitar (Figure 13).

Figure 12: The hyperbolic orbit of an object from beyond the solar system (NASA/JPL-Caltech)

Figure 13: The curve in the side of a guitar is also a hyperbola, just like the orbit shown above.

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Ideas for extending this section: ● Take a look for ellipses around you. For example, look at the top of a cup at different angles, and wheels. ● Look up online lessons on different ways to draw circles and ellipse. This is an important skill for artists, designers, and carpenters. ● Look at the shape of a guitar. The curves on an acoustic guitar body are the same shape as the orbit of the interstellar object, a hyperbola (see link below). That happens to be a good shape for improving the sound made by the guitar body. Basic geometrical shapes are found in many places around us.

Resources and references: ● Orbit shapes ○ Ellipses and grapes (Conic sections) ​ ○ How to draw an ellipse (pin and string method) (Youtube) ​ ○ Ellipse with changing eccentricities (Desmos) ​ ○ How to draw an elliptical curve with no strings or math! (Next Level Carpentry) ​ ○ Ellipse (Math is fun) ​ ○ Drawing an ellipse with a fixed major and minor axis length ○ Guitar shapes and hyperbolas ● Exoplanet orbits ○ Astronomers have discovered the largest known solar system (Science Alert) ​ ○ Upsilon Andromedae (Wikipedia) ​ ○ Comparison of our solar system with Upsilon Andromedae (European Space ​ Agency) ○ HD 20782 (Wikipedia) ​

Review and discussion questions: ● What are the two types of geometric shapes we talked about in this section? Can you give an example of where we see each around us? (Using the examples we gave is fine)

O rbit sizes

So far we’ve looked at orbit shapes, but how big are they?

The average distance from the Earth to the Sun is about 151 million kilometres. Light takes just over a second to reach our Moon, but the Sun is about 8 minutes and 20 seconds away at the speed of light. It would take a jet 20 years to fly that distance (if it could fly in space). That distance has a special name: One Astronomical Unit. We’re going to use it for comparisons.

Table 3 shows the distance of each major planet in our solar system in Astronomical Units, which are usually just called “AUs” for short. It’s handy: if you look at the distance of Mars, you

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can simply say “Mars is 1.52 times as far from the Sun as Earth is”. As you can see, Neptune’s orbit is about 30 times as wide as ours.

Table 3: Planet and exoplanet distances from their star in Astronomical Units.

Planet Distance in Astronomical Distance on soccer field Units model

Kepler 78b 0.01 19 mm

Mercury 0.39 0.76 m

Venus 0.72 1.40 m

Earth 1 1.94 m

Mars 1.52 2.91 m

Jupiter 5.20 10.09 m

Saturn 9.54 18.51 m

Uranus 19.18 37.21 m

Neptune 30.06 58.32 m

2MASS J2126–8140 4,500 (or more) 8.7 km

If you imagine that the Sun, which is 1.39 million kilometres wide, is the size of a Canadian dime, 18 mm wide, we can build a scale model on a 100 metre long field (a soccer or football field will do). On this scale, the Earth would be the size of a grain of sand. If we put the Sun at one end of the field, where would we place that grain of sand? The Earth would be just under two metres away. Saturn would be the size of a pinhead at 18.51 metres. Neptune is just past the midpoint of the field. The last column of Table 3 shows a selection of planet distances at this scale.

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Figure 14: The orbits of the planets in our solar system shown at the same scale. Image made using Universe Sandbox ​

With exoplanets we’ve seen that the planets can be larger or smaller than the planets in our solar system. What about orbits? Can they also be bigger and smaller than orbits in our solar system?

The exoplanet with the smallest orbit in our table is Kepler 78 b which is 0.01 AUs in width (1/100 the size of Earth’s orbit).

One of the solar systems with the most planets known is TRAPPIST-1. It has seven terrestrial planets that are all closer to its sun than Mercury is to our Sun! Their sun is a cool Red Dwarf, however, so the planets aren’t as hot as Mercury. These orbits are close enough together that some would look bigger than our Moon does to us without a telescope from the surfaces of their neighbours: the spacing between some of the orbits isn’t much bigger than the distance between us and our Moon. In our solar system you need a telescope to see the surface of another planet.

The exoplanet that is furthest from its star is 2MASS J2126–8140, which is at least 4,500 times bigger than Earth’s orbit, and 150 times the size of Neptune's orbit. It also orbits a Red Dwarf star.

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Ideas for extending this section: ● Build the model of the solar system on an actual soccer or football field.

Resources and references: ● TRAPPIST-1 (Wikipedia) ​ ● New class of exoplanets with orbits of less than nine hours (NASA) ​

Review and discussion questions: ● If we want to find as many planets as we can, should we just look for planets around stars like our Sun? ● Would our model solar system fit in an NHL hockey rink? (60.96m x 25.9m)? Which is better to remember the size of the solar system for our model, a soccer field or a hockey rink?

H ow long is a year on different planets?

A planet’s year is how long it takes to make one complete orbit of the Sun. If you are 11 years old, that means you’ve completed 11 trips around the Sun. How long is a year on other planets compared to an Earth year, which is 365 days?

Mercury, as you saw, is closer to the Sun than us, with an orbit that is 0.39 times as big as ours. Does that mean its year is 0.39 x 365 days = 142 days long? No! Mercury’s year is 88 Earth Days long. That’s because the closer a planet is to its star, the faster it moves in its orbit. Not only is the orbit circumference smaller, the planet moves faster.

Mars, which is further from the Sun than us, moves slower in its orbit, 24 km/s compared to Earth’s 30 km/s, and takes 686 Earth Days for every one of its years. Kepler, the same astronomer we talked about earlier who showed that planets move in ellipses, also found a mathematical relationship that described how a planet further out moves more slowly than one closer in.

How long are the years on exoplanets? To the surprise of astronomers, they found some planets that completed an entire orbit just a few hours. Those planets were much closer to their star than Mercury is to our Sun, and much hotter. There are also exoplanets with years that appear to be much longer than Neptunes. Table 4 shows the range that is known when this was written.

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Table 4: Planet years expressed in Earth Time

Planet name Year (Earth minutes, days Orbital Speed or years)

Kepler 78 b 8 hours 31 minutes 307 km/s

Mercury 88 days 47 km/s

Venus 224 days 17 hours 35 km/s

Earth 1 year 30 km/s

Mars 686 days 23 hours 24 km/s

Jupiter 11 years 313 days 13 km/s

Saturn 29 years 164 days 9.7 km/s

Uranus 84 years 7 days 6.8 km/s

Neptune 164 years 292 days 5.4 km/s

2MASS J2126-8140 905 thousand years 0.23 km/s

A ctivity Three - How old are you by different planet years?

As you already know, a day on Earth is defined by the time Earth takes to complete a full rotation on its axis. And a year on Earth is the time our planet takes to revolve around the Sun. But as you just saw, planets don’t take the same amount of time to complete an orbit around their star, and they also spin on their axes at different rates. That means that aliens living on an exoplanet would not only have a completely different definition of what’s a year, but also a day!

Even though you’ve lived a fixed amount of time, if you were born on a different planet, it will have completed a different number of revolutions around the Sun (or its host star). This means that your age would be different on other planets! Use this online calculator to determine how ​ ​ old you are in non-Earth years. Simply enter your birthday and you will see your current age on each of the solar system’s planets, as well as when your next birthday is.

Are you over 18 years old on any planet(s)? What does that tell you about the speed at which this planet orbits the Sun? Do you notice a relation between the distance of a planet to the Sun and the time it takes to complete an orbit? With this relation in mind, can you guess on which planet you would “age” the least and why?

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As you know there are 365 Earth days in an Earth year, but once again that’s not the case for all planets. Let’s start with Mars: divide your age in days by your age in years on that planet to get the number of Martian days in a Martian year. Do the same for all the other planets of our solar system. Which planet do you think has the most unusual number of days per year?

Ideas for extending this section: ● The time between Full Moons is 29.53 Earth Days. Calculate how old you are in “Moons”. Hint: you can figure out how old you are in days by multiplying your age by multiplying your age by 365. Then add the number of days since your last birthday. Finally, divide by 29.53 days.

Resources and references: ● Your age on different planets in our solar system (Exploratorium) ​

Review and discussion questions: ● Which planet would be a better place to go into the birthday cake business, 2MASS J2126-8140 or Kepler 78 b? ● If you are 11 years old, how old would you be in Kepler 78b years? (Hint, convert 11 years into minutes and then divide by the number of minutes in Kepler 78 b’s year). ● If you are under 16 on Earth, would having more birthdays on another planet be a good reason that you should be old enough to learn to drive?

D ifferent kinds of solar systems

Until the first planets were found around another star in 1992 we didn’t have anything we could compare our solar system to. We could wonder how many planets they had, and if planets were only found in systems with a single star. We are now starting to find examples of solar systems that are quite different.

In fact, those first confirmed exoplanets in 1992 were orbiting the dense, spinning core of a dead star, something called a neutron star, and are likely getting blasted with radiation lethal to life. Planets have been found around similar stars elsewhere. Most, however, are found around stars, which, like our Sun, are still shining. Some of those stars are hotter and some cooler: the closest exoplanet is found around a Red Dwarf star, Proxima Centauri, just 4.3 light years away.

Our solar system has eight major planets. So far, astronomers have only found one other solar system other than ours that has that many planets. There haven’t been any found with nine or more. If you look at this table you can see that there are many more solar systems that only have one planet compared to solar systems with many. Does that mean that solar systems with many planets like ours aren’t common? Astronomers aren’t sure. The problem is that it is hard to find small planets. This means that some of these solar systems many have more planets

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than we can currently find. At the time of writing (August 2020) NASA has listed 718 solar systems with more than one planet.

Table 5: Number of solar systems with a given number of planets (as of August 28, 2020)

Number of planets in the solar system Number of known solar systems

1 2400

2 471

3 157

4 58

5 24

6 6

7 1

8 1 (Not including ours!)

Do all solar systems just have one sun in the middle like ours? We know that’s not true, but as you can see from Table 6, about 88% of star systems known to have planets are single star systems. That seems high because only ⅔ of star systems are single star systems. How come they aren’t finding more planets in systems with more than one star?

Part of the reason we’re finding fewer cases of planets in multiple star systems is the fact that such systems are less stable. In the first activity of Unit 2, you drew a binary star system and then added planets. The planets you drew had to either be close enough to one of the two stars to “ignore” the gravity of the other, or it had to be far enough to orbit the two stars at the same time as if these were a single object.

In theory, we could have other configurations where a planet is for example alternating its orbit between the two stars (provided they’re the same mass), making sort of an 8 shape. However such orbits would be very unstable, the slightest nudge could cause the planet to get ejected out of the system. This also applies to planetesimals, which is why during the formation of the system’s planets, accretion is way trickier (if not outright impossible) in these unstable configurations. And if we have even more stars in the solar system, it’s even harder to find stable orbits, which is why such systems are less common.

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Also, it’s simply harder for technical reasons to find planets in systems with more than one star. If we are looking for the effects of a planet tugging on a star with its gravity, having other stars there doing the same thing complicates matters.

Nonetheless, planets have been found in systems with as many as four stars. In the movie Star Wars: A New Hope, Luke is living on Tatooine, a planet orbiting two stars. That movie was made about thirty years before astronomers found the first example of a planet in a binary system.

As you can see in Table 6, we now know of at least 275 solar systems that contain two stars. Star systems with four stars are not as common as systems with one or two, so you would expect to find fewer examples of quadruple star systems that also have planets.

“Rogue planets” have been found that don’t orbit any star and move through space on their own. Only two of those have been confirmed so far.

Table 6: Number of stars in a solar system (as of August 28, 2020)

Number of stars in the system Number of known solar systems

0 2

1 2802

2 275

3 39

4 4

Not every Sun is the same

You may have noticed that some of the solar systems we’ve talked about don’t have a Sun like we do. Some have remnants of massive stars that exploded, called Pulsars, while others have a Red Dwarf star. It seems that planets orbit all types of stars. The hot, massive stars are rare, however, so there are probably many more planets that have a Red Dwarf as their Sun than a massive blue giant star. Our star, as you may recall from Unit 2, is more common than blue giant stars but there are approximately eight times as many Red Dwarf stars as there are stars like our Sun, and they make up about 7 out of every 10 stars in our Milky Way Galaxy. Still, astronomers are hoping to find a solar system similar to ours so many searches pay the most attention to stars like our own. The first discovery of a solar system with a star like our own was 51 Pegasi, found in 1995. This discovery was awarded the Nobel Prize, even though it wasn’t the first exoplanet found.

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How common is our solar system?

So far, astronomers haven’t found any solar systems like ours. They had expected to find solar systems that were similar, with the rocky planets close to their sun, and gas giants further out. Instead, they found many systems with “Hot Jupiters”, gas giant planets so close to their sun that one orbit only takes a few days. That’s much closer than Mercury. There were also systems like TRAPPIST-1, which we mentioned. Finding planets as small as Mercury, Venus, Earth and Mars is harder than finding big planets like Jupiter, so that may be part of the problem: with better telescopes and techniques we might find more. But there are still fewer solar systems like ours than we expected, and many that are quite different.

There is only one star that we know of right now that has as many major planets as ours, the Kepler-90 system, which is a Sun-like star. All eight of its planets have orbits that would fit inside of Earth’s orbit, and it has rocky planets close in and gas giants further out, just like our solar system. The planet closest to its sun, Kepler 90-b, has a year that is only 7 Earth days long, and it is only .07 AUs from its sun. It is a “Super Earth” that has a mass of 2.2 times that of Earth and a diameter 1.3 times Earth’s. The sunlight there is more than 180 times as strong as it is on Earth. The planets that are at a more comfortable distance from the star are giant planets.

How many solar systems?

Our Milky Way Galaxy, as you will remember from Unit 4: The Milky Way, has hundreds of billions of stars in it. Based on the studies done so far, astronomers think there are more planets than there are stars in the Milky Way. That means that astronomers have only found 1/100,000,000 (one one hundred millionth) of all of the solar systems in our galaxy alone. New ​ ​ missions to find planets are expected to continue to find tens of thousands of new solar systems in the coming decades. While astronomers haven’t found a solar system just like ours yet, they have only just scratched the surface.

Ideas for extending this section: ● Review Unit 2: Properties of the Stars to remind yourself about different types of stars and how common multiple star systems are. ● Look through NASA’s “Exoplanet Catalogue” at the link below.

Resources and references: ● List of multiplanetary systems (Wikipedia) ​ ● Kepler 90 (Wikipedia) ​ ● Kepler 90 (NASA) ​ ● Kepler 90 b (NASA) ​ ● The variety of orbits discovered by Kepler Space Telescope (Youtube) ​ ● The Exoplanet Catalogue (NASA) ​ ● Can Two-Star systems like Tatooine exist? (Youtube) ​

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● What is the weirdest solar system you’ve found? (NASA) ​

Review and discussion questions: ● In our world ancient people could see the surface of our Moon but not other planets. Would they have referred to neighbouring worlds as wandering stars in the TRAPPIST-1 system? Would their stories have been more like our stories about our Moon? Why? ● If you had to award the Nobel Prize (considered the biggest prize in science), would you give it for the first discovery of a planet around a star like the Sun, or would you have given it for the first discovery of an exoplanet? Which happened a few years ago?

G oldilocks Zones and habitability

Scientists say that a habitable environment is one that has liquid water. While we can’t say for sure that this is a requirement for all life in the universe, we do know that this is at least true for all life on Earth.

Water must be warm enough to be in a liquid state: it can’t be all ice on a planet or all steam or water vapour.

Think back to a time when you were near a campfire or other strong source of heat like an oven. Just like an open fire, the closer a planet is to a star, the hotter it will be. How close you are makes a big difference. If you move 2 times as far away, the heat drops to ¼ ( ¼ = 1/ (2 x 2)). If ​ ​ ​ ​ ​ ​ you move 3 times as far away, the heat drops to 1/9 (1/9 = 1/(3 x 3)). If you move 4 times as far ​ ​ ​ ​ ​ ​ ​ ​ away, the heat drops to 1/16 (1/16 = 1 / (4 x 4)). This is called the Inverse Square Law. You may ​ ​ ​ ​ recall this from Unit 3 in the section “But what makes some stars visible to us and others not?”, which talked about the Inverse Square Law, but for light. You have to sit at just the right distance to feel not too warm and not too cold.

If water is on a planet that is too far from the star, it will be in the ice state. If it is close in, it will be too hot, and will be in a gaseous state. It has to be at just the right distance to be in a liquid state on the surface of the planet. Astronomers call this distance the Habitable Zone, or Goldilocks Zone because the distance is “just right” for habitability.

It’s no surprise that Earth happens to be within the Habitable Zone of the Sun. There is plenty of liquid water on it, after all! Figure 15 shows the Habitable Zone for our Solar System, with Earth in the green area, where liquid water is possible. The red portion is too hot (water is gaseous), and the blue portion and beyond is too cold (water is solid).

Figure 15: The Habitable Zone of the Solar System is shown in green. Image made using Universe Sandbox

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Is this zone the same for all stars? The answer is no, as you can see in Figure 16. Recall that stars can have different temperatures, so the distance from them that is “just right” for liquid water depends on how hot they are. If we orbited a Red Dwarf star at the distance Earth orbits our Sun, all of the water on Earth would be ice. If we orbited a hot blue giant star, all of the water at this distance would be in a gaseous state.

Figure 16: Habitable zones around stars of different temperatures (courtesy NASA/ Kepler Mission / Dana Berry)

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If a planet has an orbit with high eccentricity it can make a big difference in how much heat it receives from the Sun at different points in its orbit.

The orbit of Mercury is eccentric enough that it receives half as much heat from the Sun when it is furthest from the Sun compared to when it is closest.

What about Earth? Earth’s orbit is so close to a circle that we receive only 7% more sunlight when we are closest to the Sun. In case you are wondering, that is not in summer in Canada - instead, we are closest to the Sun during the first week of January! Our seasons are caused by the tilt of our planet, not by how close we are to the Sun. However, when our orbit was more eccentric this made a bigger difference: we received 25% more sunlight when we were closer to the Sun. This affected the Earth’s climate because in some places on Earth the seasons were much more extreme. This is not a reason why the Earth is currently experiencing global warming: the change is too slow, and our orbit is getting more circular. But even when our orbit was more eccentric we were still in the habitable zone: there was still liquid water on Earth in some places.

Remember that the most eccentric exoplanet orbit found, for planet HD 20782, is 0.95. This ​ planet orbits a star like our Sun. Let’s have a look at that. For that world, perihelion receives 1,521 times more sunlight than aphelion. At perihelion, it is 0.07 AUs from its sun - a fifth the distance of Mercury from our Sun - and at aphelion it is 1.43 AUs, almost as far out as Mars. Even though part of its orbit was in the Habitable Zone, much of it would not be, and any water on its surface would go between being completely vapourized for part of its 585 day year then completely frozen.

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But it’s not as simple as just being in the right place and having a fairly round orbit. It also depends on whether you have enough atmosphere. At high elevations, like at the top of a ￮ mountain, the air is thinner. Water boils at 100 ​ C, but only close to sea level, where the air is ​ thickest. If you took a pot of water all the way up to the very top of the CN Tower and started to ￮ heat it up, it would start to boil (turn into a gas) at around 98 ​ C. On top of Mt. Everest, water ￮ ​ boils at 68 C​ , which is about the same temperature that most people like their coffee or soup. ​ As you will remember from the last unit, Mars’ atmosphere is too thin for there to be liquid water on its surface.

Not only will water be a gas at lower temperatures and in a thinner atmosphere, but it is never a liquid in the vacuum of space. Objects in space with plenty of water ice, like comets, will be in a solid state. If they get close to a heat source, such as a star, the ice will change right from solid to gas, skipping the liquid phase all together!

If the atmosphere is too thick, it will get too hot from the greenhouse effect mentioned in the last unit.

Clearly, the atmosphere has to be “just right” as well. This is why the definition of the Habitable Zone is actually the distance from the star needed for water to be liquid on a planet with the ​ same atmosphere as Earth. Not all planets have the same atmosphere of Earth, so it is ​ entirely possible for liquid water to exist outside the Habitable Zone.

Astronomers therefore think that the planet has to be somewhere between 80% and 200% the diameter of Earth to hang onto its atmosphere, but not have so much atmosphere it turns into a mini-Neptune.

A planet could be outside the Habitable Zone, but still contain liquid water, if its atmosphere is thick enough and there is a strong greenhouse effect. Or the water could be inside the warm interior of the world like we said in the last unit about the big moons of Jupiter, and Saturn’s moon Titan.

Another problem is that while some planets have been found in the Habitable Zone of Red Dwarf stars, those types of stars can have flares of dangerous particles and also give off x-rays. There are also stars that change in brightness, so their Habitable Zone moves in and out.

There are all kinds of possibilities. Still, the Habitable Zone provides a good starting place for searching for planets similar to the Earth. We just have to remember that distance from the star isn’t the only important thing.

Ideas for extending this section:

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● Learn about the tilt of the Earth’s axis and why that is the most important factor in our seasons. ● Astrophysicist Sean Raymond created a blog where he tries to create the “Ultimate Solar System” with as many habitable worlds as possible. You’ll find a link to this page in the Resources below. Do you think such systems are likely to form naturally? Why? ​

Resources and references: ● How water can boil in a vacuum chamber at room temperature (Youtube) ​ ● What causes the seasons? (NASA Space Place) ​ ● The Ultimate Solar System (Planet Planet - Sean Raymond) ​

Review and discussion questions: ● Mars is inside the Habitable Zone in the Solar System, so why do you think we don’t see liquid water? It might help to reread parts of the last unit where we talk about Mars. ● Venus is outside the Habitable Zone (it is too close to the Sun). But if it was just inside, do you think it would have liquid water? ● Do you think animal behaviors such as hibernation might be more common in a world that has an orbit with greater eccentricity? Why?

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