Handed out: November 2, 2009
Due (in class): November 11, 2009
The rules: Collaborative work is encouraged. This homework can be done in consultation with your fellow classmates, the AI, or the professor. However, everyone must submit their own solutions to get credit, and all help should be acknowledged (a single sentence mentioning the others in your study group is sufficient). Show your work.
1. Just the facts [5 pts]
(a) [1 pts] True or False, Some meteorites found on Earth originally came from the Moon or Mars.
(b) [2 pts] What is the difference between a meteoroid, a meteor, and a meteorite?
(c) [2 pts] Why do the ion tail and dust tail of a comet point in different directions?
2. Pluto [20 pts]
(a) [4 pts] Calculate the maximum angular separation between Pluto and Charon as seen from Earth. (Assume that Pluto is at its minimum distance from the Sun and that Pluto is at opposition as seen from Earth.)
(b) [6 pts] The brightness of the Sun is inversely proportional to the square of the distance from the Sun. Compared to the brightness of sunlight on the Earth, what is the brightness (i) on Pluto at perihelion, and (ii) on Pluto at aphelion. (iii) How much brighter (percentage-wise) is it on Pluto at perihelion compared with aphelion?
(c) [10 pts] Spectroscopic observations suggest that Pluto is covered with icy frost and thus has a high albedo (0.5). As seen from Earth, the brightness of Pluto at opposition (38 AU from the Earth) is 2 x 10-17 as bright as the Sun (1 AU from the Earth). From these two observations, calculate a radius of Pluto.
3. Debris and Space Junk [25 pts]
(a) [4 pts] Suppose that a binary asteroid is observed in which one member is 16 times brighter than the other. Suppose that both members have the same albedo and that the larger of the two is 120 km in diameter. What is the diameter of the other member?
(b) [8 pts] Assume that Ida's tiny moon Dactyl (1.6 x 1.4 x 1.2 km in size) has a density of 2500 kg/m3. (i) Calculate the mass of Dactyl in kilograms (for simplicity, assume that Dactyl is a sphere 1.4 km in diameter). (ii) Calculate the escape speed from the surface of Dactyl. If you were an astronaut standing on Dactyl's surface, could you throw a baseball straight up so that it would never come down? Professional baseball pitchers can throw at speeds around 40 m/s; your throwing speed is probably a bit less.
(c) [9 pts] A very crude model of a typical comet nucleus is a cube of ice (density 1000 kg/m3) 10 km on a side. (i) What is the mass of this nucleus? (ii) Suppose 1% of the mass of the nucleus evaporates away to form the comet's tail. Suppose further that the tail is 108 km long and 106 km wide. Estimate the average density of the tail (in kg/m3). For comparison, the density of the air you breath is 1.2 kg/m3. (iii) In 1910, the Earth actually passed through the tail of Comet Halley. At the time, there was some concern among the general public that this could have deleterious effects on human health. Was this concern justified? Why or why not?
(d) [4 pts] The Kirkwood gaps (named after I.U's very own Daniel Kirkwood) are major gaps in the asteroid belt. Consider the gap which has an orbital period 1/3 of Jupiter's orbital period. Calculate the distance from the sun to this gap.