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teme92
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Homework Statement
(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?
Homework 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)##
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.
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