Problem Set 5

Home , Martian dichotomy

Problem Set 5 Formation of the moon In our global warming lecture we discussed the fact that the Earth itself was once a ‘runaway greenhouse’, because its entire surface was molten rock. The Earth was probably molten just after it formed (because of the gravitational energy it gained while forming). But, as we saw in the moon formation movies, the Earth was probably also molten just after the moon forming impact. We’re going to use this fact to estimate the mass of the moon-forming impactor. The energy of the impactor was all kinetic energy: 1 E = m v2 2 imp

(E is kinetic energy, mimp is the mass of the impactor, and v is the velocity of the impactor). A lot of this energy was converted into heat, which caused the Earth to melt. The energy required to cause the entire Earth to get to the melting point is: E = mEarthcpTmelt

(E is energy, mEarth is the mass of the Earth, cp is called specific heat, and is different for different materials, Tmelt is the melting temperature). To find out how big the impactor needed to be to melt the Earth, we equate the two expressions above and solve for mimp to find m c T m = Earth p melt imp 1 2 2 v Let T be the melting temperature of rock: 1000 K. Let v be the escape velocity from Earth: 11000 m/s. 3 And let cp be the specific heat of rock: 0.7 ×10 Joules/kg/K. Look up the mass of the Earth (in kg). Calculate the mass of the impactor required to melt the Earth

How does the mass of the impactor compare with the mass of the moon, the mass of the Earth, and the mass of Mars?

Even after rock becomes hot enough to melt, extra energy is required for the rock to change phase from solid to liquid (this is called the ‘heat of melting’). Taking this into account, would the impactor mass you estimate be bigger, smaller, or the same? Explain.

1 The impactor could have hit the Earth with a speed faster than the escape speed. Taking this into account, would the impactor mass you estimate be bigger, smaller, or the same? Explain.

The specific heat (cp) value we used above is for rock. However, the Earth has a significant amount of metal in its core, and metal has a lower specific heat than rock. Taking this into account, would the impactor mass you estimate be bigger, smaller, or the same? Explain.

Come up with at least 2 other reasons why our simple calculation is not exactly correct.

(By the way, in case you’re curious, researchers believe the mass of the moon-forming impactor was similar to the mass of Mars. Did you come close?)

Google Mars Data collected by NASA and other space organizations are always available to the public, but can sometimes be hard to access. However, the web is making a lot of the data more accessible. In this homework set, you’ll explore one tool – Google Mars – to learn about Mars’s surface. The first step is to pull up a webpage with Google Mars, which is located here: http://www.google.com/mars The first map that appears is an elevation map, created from data taken by the Mars Orbiter Laser Altimeter (MOLA), that surveyed the surface of Mars from 1997-2006. MOLA determined the height of the surface by measuring the time it took a pulse of laser light to leave the spacecraft, reflect off the surface of Mars, and return to the detectors. Zoom out on Mars until you can see the whole planet (a quirk of Google Mars is that the map “wraps” around, so you may see features repeat when you zoom out too much.) Using the MOLA map, answer the following questions: • One of the most noticeable features of the MOLA map is the difference between the northern and southern hemispheres of Mars, called the Martian Dichotomy (that’s just a fancy word for something with two different parts). Using the elevation bar on your map, what is the typical elevation of the southern highlands?

• What is typical elevation of the northern lowlands?

2 One theory to explain the appearance of the lowlands is that an ocean might have existed there in the past. We’re going to make a rough estimate of the volume of water that would be needed to ﬁll the ocean. Let the radius of the ocean be 1000 km, and the depth be the diﬀerence in height between the highlands and lowlands. Calculate the volume of the ocean using the equation for the volume of a cylinder:

Volume = height × π × radius2

• What are the heights of the polar caps (the swirling features at the top and bottom of the maps)?

• Assuming the polar caps are made from water and are 500 km in radius, calculate an approximate volume for the polar caps.

• Assuming ice and water have similar densities (which they do) could water from the polar caps have ﬁlled our hypothetical ocean?

• Besides freezing into ice caps, what else could have happened to water on Mars?

• Last week you did a crater counting activity for Mars. Looking at the diﬀerences in cratering between the northern and southern hemispheres, what can you say qualitatively about the ages of the surfaces in the two diﬀerent hemispheres?

• Hellas Basin has some of the lowest elevation on Mars. Use the search function to search for ”Hellas Basin.” What is the elevation in the bottom of the basin?

• Do you suspect Hellas Basin was formed by an impact? Why or why not?

• Type ‘Olympus Mons’ in the search bar. About how high is Olympus Mons, and how does it compare to the height of Earth’s biggest mountain (from base to height), Mauna Kea?

3 • Use the search box to search for “MER Spirit Rover ”. This will put you in Gusev Crater. What feature do you think makes scientists believe water once ﬁlled this crater?

• Use the search box to search for “Valles Marineris”. Describe how Valles Marineris is similar to or diﬀerent from the Gusev Crater water feature.

• Do you think water ﬂowed in Valles Marineris? Why or why not?

In addition to MOLA (the elevation map) Google provides a visible map and an infrared map as well. The visible map would be similar to what we’d see with our own eyes. The infrared map is the heat emitted by the surface. • Use the search box to search for “Water ice in crater at Martian north pole” and then click on the ‘Visible’ box at the upper right. What do you think is the feature in the center of the crater?

• Now click on the ‘Elevation’ box. Does this agree with your hypothesis? Explain.

• Now click on the ‘Infrared’ box. What does the feature look like and why? (Remember, infrared light is the heat emitted by the surface)