i have a problem. we have a elliptical orbit. Velocities of perigee point and apogee point is given. I have to find the eccentricity and semi major axis.
I found eccentricty with conservation of momentum. but couldn't find the semi major axis. I tried
$V_p^2$ = ($\mu$ (1+e))/ $r_p$
i found $r_p$ and $r_a$ with that formula but when I do the eccentricity formula with that radius the eccentricity is not match with the I found before.
How can I obtain the semi major axis? I am pretty sure first eccentricity is the right answer.
$$h = momentum = r_a∗V_a= r_p∗V_p$$ i know the $$V_a/ V_p$$ and with ratio of that i used $$r_p/r_a=(1−e)/(1+e)$$ with that i found e.