Satellite orbits the Earth and its perigee r_min and tangential speed at perigee v_pe are given. The problem says do not use mass of Earth in the calculation, and use the only the constants g = 9.8 and radius of Earth 6380 km. I'm supposed to find the apogee and orbital period, but not using mass of Earth makes things seem so complicated. And the formula for period itself has mass of Earth in it.
where ecc is eccentricity
perigee = r_min + radius of Earth
r_max = (1+ecc)*r_min/(1-ecc)
The Attempt at a Solution
Since argular momentum is conserved,
m v_pe r_min = m v_ap r_max
=> r_max = v_pe r_min / v_ap
I tried to find v_ap, but that the formula has mass of Earth in it, so I can't use that.
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