HELP! A satellite is orbiting the earth at an altitude where the acceleration due to gravity is 8.70 m/s2. What is its speed? 7.45x103 m/s 2.65x103 m/s 7.91x103 m/s 7.68x103 m/s

Question

A satellite is orbiting the earth at an altitude where the acceleration due to gravity is 8.70 m/s². What is its speed?

7.45x10³ m/s

2.65x10³ m/s

7.91x10³ m/s

7.68x10³ m/s

Answer 1

Let

a = 8.7 m/s² be the satellite's centripetal acceleration,

M = 5.98×10²⁴ kg be the mass of the Earth,

G = 6.674×10^-11 m³⋅kg^-1⋅s^-2 be the gravitational constant,

R (unknown) be the radius of the satellite's orbit,

v (to be calculated) be the satellite's velocity.

The satellite's centripetal acceleration

a = v²/R (1)

must equal its gravitational acceleration

GM/R²

The reason is that the centripetal acceleration is caused by gravity.

v²/R = GM/R²

v² = GM/R (2)

From (1) we express

R = v²/a

and plug it into (2)

v² = GM/(v²/a)

v = (GMa)^1/4

Plugging in actual numbers

v = (6.674×10^-11× 5.98×10²⁴ × 8.7)^1/4 = 7.68×10³