- #1
tristanslater
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Homework Statement
A satellite is in circular orbit at an altitude of 800 km above the surface of a nonrotating planet with an orbital speed of 3.7 km/s. The minimum speed needed to escape from the surface of the planet is 9.8 km/s, and G = 6.67 × 10-11 N · m2/kg2. The orbital period of the satellite is closest to
Homework Equations
This question is supposed to be related to Kepler's law, so I imagine it has something to do with:
##k = \frac{T^2}{R^3}##
Another period equation I've tried:
##T = \frac{2\pi\sqrt{R}^3}{\sqrt{GM}}##
I think energy is going to factor in somehow, so:
##K = \frac{1}{2}mv^2## and ##U = \frac{GMm}{R}##
And escape velocity is given, so maybe:
##v_e = \sqrt{\frac{2GM}{R}}##
The Attempt at a Solution
Everything I try, it seems like there is not enough information.
I tried starting with:
##T = \frac{2\pi\sqrt{R}^3}{\sqrt{GM}}##
Then I solved the escape velocity formula for ##\sqrt{GM}##:
##\sqrt{GM} = v_e\sqrt{\frac{R}{2}}##
This way I can sub it into the perio equation:
##T = \frac{2\pi\sqrt{r}^3}{v_e\sqrt{\frac{R}{2}}}##
Simplifying I get:
##T = \frac{2\pi R\sqrt{2}}{v_e}##
This gets rid of most of the unknowns, but it still contains R, which we don't know. This is where I get stuck. How can we find a substitution for R?
Thanks.