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AST 105 HW #11 Solution
Week of November 2nd, 2015
Note: All Problems are from The Cosmic Perspective (6ed)
Chapter 12
Review Problems
2. How does the largest asteroid compare in size to the planets? How does the total mass of all asteroids
compare to the mass of a terrestrial world?
 Even the largest of asteroids, Ceres, is small compared to the planets. (Ceres's diameter is less than
half that of Pluto.) So despite the large number of asteroids, their masses add up to a small fraction
of the mass of any of the planets.
3. Where is the asteroid belt located, and why? Briefly explain how orbital resonances with Jupiter have
affected the asteroid belt.
 The asteroid belt is located in-between the orbits of the Mars and Jupiter. The asteroid belt exists
because of orbital resonances with Jupiter. In that region of the solar system, Jupiter's resonances
pump up the eccentricities of objects, making their collisions high speed. This keeps them from
clumping together and forming a planet. In fact, it tends to make the asteroids break apart when
they collide.
Test Your Understanding
Suppose someone claimed to make the discoveries described below. (These are not real discoveries.) Decide
whether each discovery should be considered reasonable or surprising. Explain clearly; not all these have
definitive answers, so your explanation is more important than your chosen answer.
15. A small asteroid that orbits within the asteroid belt has an active volcano.
 This discovery is unexpected. Even the largest of asteroids, Ceres, is too small to be geologically
17. An object that resembles a comet in size and composition is discovered orbiting in the inner solar
 This is reasonable. Many comets from the outer solar system have their orbits altered so they
become locked in the inner solar system. But exposed ices would be used up in a few years, so the
object might not last long or might become covered in a protective layer of dust.
Investigate Further
38. The Role of Jupiter. Suppose that Jupiter had never existed. Describe at least three ways in which our
solar system would be different, and clearly explain why.
 Here are some possibilities.
1) The asteroids might have accreted into a single planet between Mars and Jupiter.
2) The asteroid belt would not have gaps.
3) Fewer comets would have been ejected into the Oort cloud, leaving many more that could
potentially impact Earth
40. Asteroid Discovery. You have discovered two new asteroids and named hem Albert and Isaac. Both lie at
the same distance from Earth and have the same brightness when you look at them through your telescope,
but Albert is twice as bright as Isaac at infrared wavelengths. What can you deduce about the relative
reflectiveness and sizes of the two asteroids? Which would make a better target for a mission to mine
metal? Which would make a better target for a mission to obtain a sample of a carbon-rich planetesimial?
 Because Albert emits a higher proportion of thermal emission (infrared) than of reflected light
(visible), it must be warmer than Isaac. This means it must be darker (in order to be warmed by the
Sun). Because Albert has a lower reflectivity than Isaac, it must be larger in order to appear as
bright. Isaac would make a better candidate for mining metal, and Albert a better candidate for
carbon-rich material.