Dietrichw
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Homework Statement
Show that the rate of change of the free-fall acceleration with vertical position near the Earth's surface is
\frac{d}{dr} [g] = -\frac{2GM_E}{R_E^3}
Assuming h is small in comparison to the radius of the Earth, show that the difference in free-fall acceleration between two points separated by vertical distance h is
\Delta g = \frac{(2GM_E h)}{R_E^3}
Show that the minimum period for a satellite in orbit around a spherical planet of uniform density ρ is
T_{min} = \sqrt{ \frac{3\pi}{Gp}}
Homework Equations
g=\frac{GM_E}{R_E^2}
T^2=Kr^3
The Attempt at a Solution
I did the first one easily
\frac{d}{dr} [\frac{GM_E}{R_E^2}]
\frac{d}{dr} [GM_E R_E^{-2}]
simple power rule
The second and third not so much, I substituted one R with (R+h) as that is what it seems like is going on and find the difference. That did not work out for me
The third I thought about p= Mass/Volume and solving for R and substitute but I'm not sure what to do with K and Kepler's 3rd observation is the only equation that I have the deals with the period
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