Posted by carlton on Saturday, October 22, 2011 at 11:02pm.
(a) First you need the value of the acceleration of gravity at the orbit location. Call it g. Here are the steps.
Moon radius = Rm = 1.7*10^6 m
Orbit height = H = 7.2*10^5 m
Orbit radius = R = Rm + H
= 2.42*10^6 m
R/Rm = 1.424
gm (at moon's surface) = 0.839 m/s^2
g(at orbit radius location) =
gm/(1.424)^2 = 0.414 m/s^2
Now set M g = M V^2/R
Satellite mass M cancels out.
V^2 = (R*g)
V = 1000 m/s
(b) orbit period = 2*pi*R/V
= 15,210 s
= 4.2 hours
(a) First you need the value of the acceleration of gravity at the orbit location. Call it g. Here are the steps.
Moon radius = Rm = 1.7*10^6 m
Orbit height = H = 7.2*10^5 m
Orbit radius = R = Rm + H
= 2.42*10^6 m
R/Rm = 1.424
gm (at moon's surface) = 0.839 m/s^2
g(at orbit radius location) =
gm/(1.424)^2 = 0.414 m/s^2
Now set M g = M V^2/R
Satellite mass M cancels out.
V^2 = (R*g)
V = 1000 m/s
(b) orbit period = 2*pi*R/V
= 15,210 s
= 4.2 hours
The acceleartion due to Gravity is already given at the orbital height. Proceed to use to value of gravitational acceleration given of 0.839m/2^2. The rest of the strategy is all good.
-m
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