## APAS 1010

### Problem Set #2

DUE TUESDAY, MARCH 4, 1997

A. Most of the asteroids are contained between 2.06 AU and 3.27 AU.

1. What resonance of Jupiter establishes the inner edge at 2.06 AU?
2. What is the period of those asteroids at the inner edge?
3. What resonance of Jupiter establishes the outer edge at 3.27 AU?
4. What is the period of those asteroids at the outer edge?
B. The most dangerous asteroids are the earth-crossing asteroids, (also known as Apollo asteroids) which have elliptical orbits that carry them from the inner portions of the asteroid belt across space to the earth's orbit. One such asteroids of the largest is named Sisyphus which has a diameter of 9 km (it could do lots of damage and could even wipe out Dallas.) and a mean distance of 1.89 AU.

5. How often does Sisyphus cross the earth's orbit?

C. Extinction events on the earth, caused by asteroid or comet impacts, appear to occur every 30 million years. At those times a "DEATH STAR" may send a rain of comets into the inner solar system. That star may be in orbit around the sun; too faint and too distant to be easily seen, but gravitationally powerful enough to nudge comets out of the Oort comet cloud.

6. What is the DISTANCE of such a hypothetical death star? Where is it located with respect to the Oort cloud?