Explorations: An Introduction to Astronomy (Arny), 7th Edition

Chapter 11: Small Bodies Orbiting the Sun

Problems

1
The speed with which a meteoroid hits the atmosphere is roughly the speed of the Earth in its orbit (you might say the Earth hits the meteoroid). Show that the speed of the Earth in its orbit is about 30 kilometers/second.
2
Calculate the surface gravity and escape velocity for Ceres, assuming it has a radius of 487 kilometers and a mass of 9.43 × 1020 kilograms.
3
The asteroid Icarus has an elliptical orbit that carries it between 0.19 and 1.97 AU from the Sun. What is its semimajor axis? How oft en does it cross the Earth's orbital radius?
4
Show that Pluto's orbital period is very close to one and one-half times Neptune's. Use the data in the appendix.
5
Use the modified form of Kepler's third law to calculate the mass of Pluto and Charon from the orbital data for Charon given in the text (unlike in problem 2, the satellite's mass is about 12% of the planetoid's mass, so we will not neglect it here). Compare your result to the sum of the masses given for Pluto and Charon in the appendix. Be sure to convert the orbital period to seconds and the orbital radius to meters before putting those numbers into the formula.
6
Calculate the density of Charon, given that its radius is approximately 600 kilometers and its mass is about 1.5 × 1024 grams. (Be sure to convert kilometers to centimeters or meters.) Is it likely that Charon has a large iron core? Why?
7
Comet Swift -Tuttle has a period of about 133 years and leaves the debris that causes the Perseid meteor shower. Calculate the semimajor axis of the comet's orbit. If the orbit is highly elliptical, approximately how far from the Sun is the comet at aphelion? What is found at this distance?
8
Use Kepler's third law to determine the period of a comet whose orbit extends to 50,000 AU, within the inner Oort cloud.
9
Given that the temperature of a body decreases as the square root of its distance from the Sun increases, estimate the temperature of a comet nucleus in the Oort cloud. Take the temperature at 1 AU to be 300 kelvin.
10
Use the formula for kinetic energy of a moving body to estimate the energy of an SUV (mass about 2700 kilograms) traveling at 65 miles per hour (you'll need to do a few conversions on units). Compare this to the kinetic energy of a 0.010-kilogram meteoroid (about as heavy as two quarters) that collides with the Earth at 30 kilometers/second.
11
Calculate the kinetic energy of impact of a 1000-kilogram (roughly 1-ton) object hitting the Earth at 30 kilometers per second. Express your answer in kilotons of TNT, using the conversion that 1 kiloton is about 4 × 1012 joules. Be sure to convert kilometers/second to meters/second.
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