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AdkinsJr
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Homework Statement
We are to place 1000 kg satellite in circular orbit 300 km above Earth's surface...find speed and period...
Homework Equations
[tex]F_g=ma_c=\frac{GMm}{R^2}[/tex]
[tex]a_c=\frac{v^2}{R}[/tex]
Kepler's Third Law and Constant for Earth:
[tex]K_E=2.97*10^{-19}s^2/m^3[/tex]
[tex]T^2=K_Ea^3[/tex]
The Attempt at a Solution
This is all very straight forward, except the values I obtain are not consistent using both methods. I can use Newtons second law for centripetal motion to solve for v obtaining:
[tex]v=\sqrt{\frac{GM}{R}}=\sqrt{\frac{(6.67*10^{-11})(5.97*10^{24})}{6.67*10^{6}}}≈7.7*10^3 m/s[/tex]
R is the Earth radius PLUS the height above the Earth's surface. The period:
[tex]T=\frac{2\pi r}{v}≈5.4*10^3 s[/tex]
If I apply Keplers 3rd law, I have:
[tex]T=\sqrt{(2.97*10^{-19})(6.67*10^6)^3}≈9.4 s[/tex]
I can't tell where I'm going wrong here. The fast orbit is preposterous. My instructor accepted the value on my homework I obtained using second law; but I'm just reviewing the homework and tried the Kepler equation and it doesn't work...it should work though because Kepler's third law can be derived from the inverse square law of orbits.
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