Astronomy HOMEWORK Chapter 5 - 9th Edition

2. Pluto is most similar in composition which of the following objects? a. Eris; b. Jupiter; c. our Moon; d. Earth; e. the Sun. Pluto is most similar to Eris, a. Both Kuiper Belt Objects are a mixture of ices and rock, which is typical of Kuiper Belt Objects (abbreviation KBO). Earth and Moon are mostly rock and metal. Jupiter and the Sun are mostly gaseous elements. (Check your understanding: why “ices,” in the plural?)

6. Which giant planet formed first? According to the Nice model, Jupiter. Additional remark is that (according to the model) it formed somewhat OUTSIDE its current orbit. This is in contrast to the other giant plabets, which formed inside their current orbits.

7. According to the Nice theory, where did the Kuiper Belt Objects and Oort Cloud Objects come from? The KBO and OCO are icy planetesimals that were flung outward by encounters with the giant planets.

9. Jeans instability is responsible for what event in the life of the solar system? The Jeans Instability is responsible for the collapse of the solar nebula to form the Sun, as well as the rest of the solar system.

13. What two properties of a planet must be known to determine its average density? How are these properties determined? Density is mass divided by volume. So, the two quantities are mass and volume. To measure mass, astronomers measure the orbital periods of the planet’s moons along with the orbital distances of their moons. They then apply Kepler’s Third Law, in its generalized form, P 2 = (4π2/(GM)) a3, where the M is the mass of the planet. (In this form of the equation, quantities are in standard scientific units: period in seconds, semimajor axis in meters, and mass in kilograms.) The data are used to find M. The volume is determined by measuring the diameter of the planet, by measuring the diameter of its image at known magnification. The formula for the volume of a sphere is V = (4/3)πr3. So: what about Venus and Mercury, which have no moons? Astronomers measure their influence on other planets, primarily Earth, and by their deflection of comets that pass near them. This is less accurate: Venus’ mass was uncertain to several percent and Mercury’s to 15 percent in the 1920s and 1930s. In more modern times, spacecraft have flown by these or orbited them, allowing more accurate measurements. Note that using spectroscopy to identify the elements and chemicals on the surface doesn’t help much – the composition of the interior is very different from that of the surface, and planets are mostly interior, very little surface layer.

16. What is significant about the snow line described in this chapter? Inside the “snow line,” it was too hot for volatile substances (such as water, methane, carbon dioxide, and ammonia) to survive. These susbtances would be heated and sublimate [go directly from solid to vapor]. The radiation pressure from the Sun would drive them away. Outside the snow line, these could remain frozen solid, allowing them to survive. This marks the difference between rock-and-metal objects (terrestrial planets and asteroids) and objects which have in addition volatile substances (giant planets and comet nuclei).

17. What if Earth had a highly elliptical orbit, like Mercury? (20%) What would be different about Earth and life on it? With a 20% eccentricity, the solar heating would vary from 64% to 144% of average. (The student is not expected to be able to calculate those numbers). In this case, the seasons would be produced by distance from the Sun. These are more extreme than what we have now, so lifeforms would have an extremely difficult time. 24. Search the Web for information about the cool, dim star Gliese 581. What is its mass compared to our Sun’s? How bright is it (its luminosity) compared to the Sun? How many planets are known to be orbiting it? How do their masses compare to Earth’s? What is special about Gliese 581c? Googling this and checking Wikipedia on Feb 23, 2011: Gliese 581 has a mass of 0.31 that of the Sun and a luminosity of 1.3% that of the Sun. Six planets are believed to be orbiting it. Gliese 581c has a mass of about 5 times that of Earth, making it very Earth-like. Later studies suggest the existence of 5th and 6th planets, one of which is well in the star’s habitable zone – meaning close enough to have liquid water but not so close as to boil it away. Update as of Feb 28, 2012: Gl581c seems to be a little too close, like Venus. The excitement has shifted to a smaller 7th planet Gl581g, right in the middle of the habitable zone. However, the exsitence of this planet is disputed.