# Semi-major axis of an Orbit

1. Aug 6, 2015

### teme92

1. The problem statement, all variables and given/known data
(a) A satellite is initially in a geostationary orbit around the Earth, so that the satellite always remains above the same point on the Earth’s equator. Show that the radius of the orbit is $4.22\times 10^7$

(b)An engine is briefly fired in the direction of the satellite’s motion, making the speed of the satellite suddenly increase to a speed $v_p$ and sending the satellite into an elliptical orbit with eccentricity $e = 0.35$. What is the semi-major axis of the new orbit?

2. Relevant equations
Period: $T=2\pi\sqrt{\frac{r^3}{GM_E}}$

Escape Velocity: $V_{esc}=\sqrt{\frac{2GM_E}{r}}$

Eccentricity: $e=\sqrt{1+\frac{2{\epsilon}L^2}{(GM_E)^2}}$

$e=\frac{r_a-r_b}{r_a+r_b}$ where $r_a=a(1-e)$ and $r_b=a(1+e)$

3. The attempt at a solution
Done the (a) part straight forward enough with the period formula.
So I subbed in my values to get:

$r=4.22\times 10^7 m$

$V_{esc}=4345 ms^{-1}$

What I don't understand is how to get the semi major axis. If someone could point me in the right direction that would be great. I think I have to get the new period of the orbit but I don't know how.

Last edited: Aug 6, 2015
2. Aug 6, 2015

### SteamKing

Staff Emeritus
Have you posted the complete problem statement and/or all the information you were furnished?

3. Aug 6, 2015

### teme92

Hey SteamKing I edited my post and put in more,I didn't think it was necessary sorry.

4. Aug 6, 2015

### SteamKing

Staff Emeritus
It normally wouldn't make a difference if this were Psychic Forums, rather than Physics Forums.

5. Aug 6, 2015

Ouch

6. Aug 7, 2015

### andrevdh

Hint: The transfer occur at perihelion.

7. Aug 7, 2015

### teme92

What do you mean by transfer?

8. Aug 7, 2015

### andrevdh

From the one orbit to the other.