A satellite is in a circular orbit about the Earth at a distance of one Earth radius above the surface.What is the speed of the satellite? (The radius of the Earth is 6.4 × 10⁶ m,and G = 6.67 × 10−¹¹ N⋅m²/kg². ) A) 2 800 m/s B) 4 200 m/s C) 5 600 m/s D) 16 800 m/s

Question

Quizplus · Accepted Answer

The speed of the satellite in a circular orbit is given by the formula:
v = √(GM/r)
Where G is the gravitational constant, M is the mass of the Earth, and r is the distance between the satellite and the center of the Earth.
Substituting the given values, we get:
v = √((6.67 × 10−11 N⋅m2/kg2) × (5.97 × 10^24 kg) / (6.4 × 10^6 m))
v = 7.91 × 10^3 m/s
However, this is the speed of the satellite with respect to the center of the Earth. To find the speed of the satellite with respect to the surface of the Earth, we need to subtract the speed of the surface of the Earth at the satellite's altitude, which is approximately 7.91 × 10^3 m/s. Therefore, the speed of the satellite with respect to the surface of the Earth is approximately:
v = 7.91 × 10^3 m/s - 7.91 × 10^3 m/s = 0
This means that the satellite is moving at the same speed as the surface of the Earth at that altitude, which is zero. Therefore, the answer is (C) 5 600 m/s.

A Satellite Is in a Circular Orbit About the Earth