Equate the gravitational force, given by
F=GMm/r²
and the centrifugal force due to the angular velocity ω
F=mrω²
In SI units,
G = 6.674×10−11 N m² kg -2
Mass of the earth = 6*1024 kg (approx.)
r = 250 miles plus the radius of the earth to be converted to metres.
The formula for both gravitation and centrifugal force use r from the centre of the earth.
Solve for ω and calculate the period and speed.
The shuttle's mass, m, is immaterial since it will cancel out on both sides of the equation.
The space shuttle is in a 250 mile high orbit. What are the shuttle's orbital period, in minutes and its speed?
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