Question
The space shuttle is in a 250 mile high orbit. What are the shuttle's orbital period, in minutes and its speed?
Answers
MathMate
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<sup>−11</sup> N m² kg <sup>-2</sup>
Mass of the earth = 6*10<sup>24</sup> kg (approx.)
r = 250 miles <i>plus the radius of the earth</i> 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.
F=GMm/r²
and the centrifugal force due to the angular velocity ω
F=mrω²
In SI units,
G = 6.674×10<sup>−11</sup> N m² kg <sup>-2</sup>
Mass of the earth = 6*10<sup>24</sup> kg (approx.)
r = 250 miles <i>plus the radius of the earth</i> 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.