Suppose that a satellite is in a circular orbit at a height of 2.00 * 10⁶ m above Earth's surface. What is the speed of a satellite in this orbit? A) 8.31 * 10¹ m/s B) 6.90 * 10³ m/s C) 4.76 *10⁷ m/s D) 9.62 * 10⁴ m/s E) 1.41× 10⁴ m/s

Question

Quizplus · Accepted Answer

The speed of a satellite in a circular orbit is given by v=√(GM/r), where G is the gravitational constant, M is the mass of the Earth, and r is the radius of the orbit (equal to the distance from the center of the Earth to the satellite, which is the sum of the radius of the Earth and the height of the satellite above its surface).

Plugging in the given values, we get:

v=√[(6.67×10^-11 N(m^2/kg^2)×5.97×10^24 kg)/(6.38×10^6 m + 2.00×10^16 m)]
v=√[(3.98×10^14)/(6.38×10^6 + 2.00×10^16)] 
v=√(6.24×10^2) 
v=24.95×10^1 m/s 
v=6.90×10^3 m/s, which is approximately equal to 6.90×10^3 m/s.

Therefore, the best choice is B.

Suppose That a Satellite Is in a Circular Orbit at a Height