Homework #3 Solutions Ch. 7, #23 The next mission to Mercury photographs part of the surface never seen before and detects a vast field of sand dunes. Is this reasonable or surprising? Explain. This would be surprising. Our current observations of Mercury show it covered by craters, and absolutely barren of water or an atmosphere. Since sand dunes are built up by erosion cause either by winds of an atmosphere or of currents in water, we therefore wouldn’t expect to see sand dunes since we see neither water nor air on Mercury,. However, it would not be completely impossible for us to find sand dunes on Mercury. Perhaps at one point in Mercury’s history there was an appreciable atmosphere. Maybe that atmosphere and its winds were able to create sand dunes before the intense heat of the sun, and the low gravity of Mercury caused that atmosphere to evaporate away. Once the atmosphere was gone, then like the footprints of astronauts on the moon, there would no longer be any erosional forces to get remove them (asides from bombardment of meteorites – which would erase the dunes). This second case would be extremely unlikely, since that wouldn’t explain why we don’t see any dunes on the portions of Mercury that we have observed. It’d also just be too hot that close to the Sun, and Mercury doesn’t have nearly enough mass to hold a considerable atmosphere of the scale necessary, or for long enough time, to create dunes.

Ch. 7, #33 Which heat source continues to contribute to the Earth’s internal heat? The best answer is (b). Accretion (a) is the falling of matter on to a planet (or star, etc.). So, for the Earth, meteorite impacts would be a form of accretion. This is an important factor that heated up the Earth during its formation – when planetesimals were still slamming into the Earth at high speed, generating a large amount of heat. However (and luckily for us), large meteorites no longer constantly hit the Earth and thus cannot be responsible for the heating of the Earth. They also would be impacting the surface of the Earth, and wouldn’t be responsible for the internal heating of the Earth. It is true that sunlight (c) is the primary thing warming up Earth’s atmosphere and the surface of the crust, but that sunlight cannot penetrate deep into the crust – let alone 6,000 kilometers down to the Earth’s core. Radioactive decay (b) is the correct answer. Radioactive materials make up a small, but important, part of the Earth’s metals and rocks. That, combined with the Earth’s larger size and

crust that acts to insulate the interior, helps to keep the Earth warm. Out of all the answers, this is the only one that can explain the current interior heat of the Earth.

Ch. 7, #36 Which describes our understanding of flowing water on mars? Water on the surface of Mars was once important, but no longer is (b). When examining the surface of Mars we see a number of geological features, such as dry river beds and sediment deposits that appear to have been created by once flowing water, consequently showing that it was important at one time. However, due to the loss of some of Mars’s atmosphere, all or most of the surface water boiled away. Currently, some water can still be found in the polar ice caps and also perhaps underneath the surface soil, and can in very rare circumstances seep out, and cause some erosion (as seen in fig. 7.31). This is by far a minor effect and is not a major process on the surface of Mars today.

Ch. 7, #37 What do we conclude if a planet has few impact craters of any size? If we do not see many impact craters of any size, then there must be some sort of geological process erasing the craters (c). All of the bodies in our solar system underwent a period of heavy bombardment early in their formation – so at one point, all the planets had a significant number of craters of varying size. If we don’t see many craters, then something such as volcanism, tectonics, or erosion, must have erased them from the surface of the planet. It is not likely that the atmosphere screened out all of the asteroids. On the Earth and Mars, the atmosphere is appreciable, but not enough to stop all incoming asteroids or comets, as evident by the fact that we do see impacts on the surface. Even Venus, with its super dense atmosphere, has craters on the surface (although they are preferentially very large, since all the smaller asteroids and comets were burned up by the atmosphere). So even if you have a very, very dense atmosphere, there are still going to be some objects that still make it through – and that’s why (c) is a better choice than (b).

Ch. 8, #15 Suppose someone made the claim that Neptune’s deep blue color is not due to methane, but is instead do to the surface being covered completely by liquid water. This would be an extremely surprising discovery. Neptune is at a distance of about 30 AU, and is extremely cold. The cloud top temperature is only 60 Kelvin. If the “surface” of Neptune were liquid water, it would likely just freeze solid – and as you know (from just looking

at what color snow, or the polar ice caps are), this would result in a very bright, white, Neptune, and not a blue one. One way that you could get liquid water would be if the ocean was buried under enough atmosphere, such that the pressure was high enough to keep it liquid. But if that were true, then it probably be buried under such a large atmosphere that you wouldn’t see it anyway. It just makes more sense that Neptune’s color comes from its methane rich atmosphere.

Ch. 8, #24 Which lists the Jovian planets in order of increasing distance from the sun? The correct answer is (c): Jupiter, Saturn, Uranus, Neptune. (a) is incorrect because it includes Pluto, which is not a planet – let alone a Jovian planet. (b) is just the wrong order: Jupiter’s closer than Saturn.

Ch. 8, #29 Why is Io more volcanically active than our moon? Io is more volcanically active because it has a different internal heat source (c). Io is about the same size as our moon (so (a) is incorrect), and since it’s not that large, there’s not enough radioactive material within to create much ongoing heat (so (b) is incorrect). The source of this internal heat source is tidal heating, due to Jupiter and also the resonance of Io’s orbit to Europa and Ganymede – all of which pull and stretch Io, creating an internal heat source through that friction.

Ch. 8, #41 a) Io loses 1,000 kg of sulfur dioxide per second to Jupiter’s magnetosphere. Find the mass lost in 4.5 billion years. Rate at which it’s loosing mass: Time we want to look at: Converting the Time into seconds:

Amount of Mass Lost:

Let’s compare the mass lost to over this time to the mass of Io, as given by Table E.3:

This is the fraction of Io’s total mass lost to Jupiter’s magnetosphere.

b) Assume that sulfur dioxide makes up 1% of Io’s mass. When Io run out of sulfur dioxide at this present rate? Mass of sulfur dioxide:

Rate of Sulfur Loss (from part a) Time till loss of sulfur dioxide:

This is the time it will take for Io to expend its source of sulfur dioxide gas.

Ch. 7, #53 (EXTRA CREDIT) An asteroid 1 kilometer in diameter makes a crater of about 10 kilometers. How much kinetic energy does the asteroid have if it strikes the surface at 20 kilometers per second? Kinetic energy is defined as: Now, we’re given the velocity: We’re given the diameter:

The problem here is that to calculate the kinetic energy, we need the mass – however, we’re not given it. To estimate the mass, we’re going to assume that the asteroid has the density of rock, and we’re also going to approximate it as being a sphere. Density of rock: Volume of the asteroid: Now calculating the mass:

Now plugging that into these things into the kinetic energy equation:

Let’s convert this to megatons of TNT

The largest nuclear weapons have energies of about 100 megatons TNT. So, the energy of this asteroid impacting is about 1000 times more powerful than our most powerful nuclear weapons.