Question

QUESTION 13 

A satellite is in Earth orbit with an altitude at perigee of 500 km and an altitude at apogee of 700 km. 

What is the Eccentricity of the orbit?

QUESTION 15 

What is the radius of the moon's Sol relative to Earth? 

   Assume: 

     • The mass of the earth is 81.3 times the mass of the moon 

     • The semi-major axis of the moon's orbit about the earth = 3.884 x 10⁵km 

Answer 1

Radius of Moon's SOI relative to earth is

r= a(m/M )^ 2/5 where m is moon mass and M is Earth's mass

Here given M = 81.3 m and a= 3.884*10^5 km

So r = 3.884*10^5(1/81.3)^ 2/5

r= 66871.8 km, is required radius of SOI.

13.

Since we know.,

Apogee= A= a( 1+e)

And perigee P= a(1-e) , where e is eccentricity and a is semi major axis.

So A/P= 1+e/(1-e)

7(1-e)= 5(1+e)

7-7e= 5+5e

2= 12 e

e= 2/12 or 0.1667