Question

A satellite is in a circular orbit around Earth with an altitude equal to 2.50 times Earth's radius. What is the magnitude of the centripetal acceleration of this satellite? [Hint: you do not need to look up Earth's mass or radius to solve this one.]

can you solve this?

Answer #1

The velocity of the satellite, v = SQRT[(G * M) / h]

Where G is the universal gravitational constant, M is the mass of
the earth and h is the satellite's altitude

Substituting h = 2.5 * R,

v = SQRT[(G * M) / (2.5 *R)]

Squaring,

v^{2} = (G * M) / (2.5 *R)

Centripetal acceleration, a_{c} = v^{2}/h

= v^{2} / (2.5 * R)

Substituting the value of v^{2},

a_{c} = 1 / (2.5 * R) [(G * M) / (2.5 *R)]

= (G * M) / (6.25 *R^{2})

= 1 / 6.25 * [(G * M) / R^{2}]

= 1/6.25 * g

Where g is the acceleration due to gravity.

a_{c} = 9.81 / 6.25

= **1.57 m/s ^{2}**

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