Suppose the space shuttle is in orbit 310km from the earths surface, and circles

Question

Suppose the space shuttle is in orbit 310km from the earths surface, and circles the earth about once every 90.7 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g, the gravitational acceleration at the earths surface. Suppose the space shuttle is in orbit 310km from the earths surface, and circles the earth about once every 90.7 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g, the gravitational acceleration at the earths surface.

Explanation / Answer

Radius of Earth = 6,380 kilometres (approx), so if we assume that the orbit is a circular one (unlikely in practice), it will have a radius (r) of 6380 + 310 = 6690km.

The angular velocity (w) of the shuttle is 2*pi/(90.7*60) = 1.154*10^-3rad/s

centripetal accn is r*w^2 = (6690*10^3)*(1.154*10^-3)^2 = 8.909m/s^2

g = 9.81, so 8.909m/s^2 corresponds to 8.909/9.81 = 0.908g

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