Consider a spacecraft in an elliptical orbit around the earth. At the low point,
ID: 1980038 • Letter: C
Question
Consider a spacecraft in an elliptical orbit around the earth. At the low point, or perigee, of its orbit, it is 400 { m km} above the earth's surface; at the high point, or apogee, it is 4500 { m km} above the earth's surface.a)What is the period of the spacecraft's orbit?
T=8250
b)Using conservation of angular momentum, find the ratio of the spacecraft's speed at perigee to its speed at apogee.
=1.6
c)Using conservation of energy, find the speed at perigee and the speed at apogee.
d)It is necessary to have the spacecraft escape from the earth completely. If the spacecraft's rockets are fired at perigee, by how much would the speed have to be increased to achieve this?
e) What if the rockets were fired at apogee?
Explanation / Answer
2. Relevant equations Kepler's 3rd Law: T=(2*pi*a3/2)/ sqrt(GME) where a=semi-major axis 3. The attempt at a solution So the first thing I did was find the semi-major axis (value a of the eqn above): (1/2)*(4000+400)=2200 km or 2.2*106 m Then I plugged it into the equation along with the following constants: G=6.67*10-11 m2/kg2, ME=5.97*1024kg T=(2*pi*2.2*10(6)3/2)/ sqrt(6.67*10-11*5.97*1024)= 1027 seconds