PH 322 Celestial Mechanics Fall 1998 Homework Set 8. Due Thursday November 5, 1998

1. Earth is to be struck on January 1, 2002 by a piece of solar system rock such as to leave a crater the size of Rhode Island. At that instant, Earth's coordinates will be (-1,0) a.u. with respect to the Sun. On January 1, 1999 the rock will have coordinates (0,9.7) a.u. with respect to the Sun. Exactly 3 years later it will collide with Earth if not deflected by some fabulous piece of work, namely an impulse delivered to deflect the rock early enough.

You must construct an intercept out in space, half a year before scheduled impact. The intercepting spacecraft will be launched half a year after January 1, 1999 and will travel 2 years to reach the intercept point.