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.
- a) (5) Determine the orbit of the rock. Assume only the Sun acts gravitationally
on the rock. (Give values of p and e and initial theta; plot the trajectory
of the rock)
- b) (5) Locate the the space rock half a year from scheduled intercept,
1/2 year before Jan 1, 2002.(Give its x and y coordinates, or its r, theta
coordinates 1/2 year before Earth is to be struck)
- c) (5) Determine the orbit of an intercept launched from Earth on half
a year after Jan 1, 1999. This will travel 2 years to the intercept point.
(give p and e and initial theta of interceptor)
- d) (5) Determine the additional velocity components to be added to
the interceptor, above and beyond Earth's velocity ( r delta-theta/dt,
and delta-dr/dt).
- e) (5) optional 'quality' points for quality of work on the problem.
This includes plot for interceptor to intercept point. And plot showing
that rock and interceptor reach intercept at same time.