# Find the apogee from v at perigee, perigee, g, and the radius of Earth

## Homework Statement

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.

## Homework Equations

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.
Thank you

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gneill
Mentor
But given g and the radius of the Earth you can infer the gravitational parameter $\mu = GM_e$, right?

But given g and the radius of the Earth you can infer the gravitational parameter $\mu = GM_e$, right?
So what you meant is
g = GM/r_earth^2 = μ/r_earth^2
=> g*r_earth^2 = μ ? That makes sense. Thank you.

• gneill
gneill
Mentor
So what you meant is
g = GM/r_earth^2 = μ/r_earth^2
=> g*r_earth^2 = μ ? That makes sense. Thank you.
Yup. And so you can proceed with the rest of the usual basic orbital motion equation lexicon.

• Natchanon