Question

A 2400 kg satellite is in a circular orbit around a planet. The satellite travels with a constant speed of 6670 m/s. The radius of the circular orbit is 8.92x10^6. What is the acceleration of the satellite?

A) 2.5 m/s^2
B) 21 m/s^2
C) 9.8 m/s^2
D) 5.0 m/s^2
E) 0 m/s^2

Answer 1

The satellite's acceleration is calculated using the formula a = v²/r, with the velocity given as 6670 m/s and the orbit radius as 8.92×10¶ m. Calculating with these values, the resulting acceleration is approximately 0.559 m/s², which does not match the provided options, suggesting a possible error in the question's multiple-choice answers.

Step-by-step explanation:

The acceleration of a satellite in circular orbit can be determined using the formula for centripetal acceleration, which is a = v²/r, where a is the acceleration, v is the velocity, and r is the radius of the orbit. In this case, the satellite travels with a constant speed of 6670 m/s and the radius of the circular orbit is 8.92×10¶ m. Plugging these values into the formula, the calculated acceleration is:

a = (6670 m/s)² / (8.92×10¶ m) ≈ 4988.9 m/s² / 8.92×10¶ m ≈ 0.559 m/s²

This result does not match any of the options provided in the question. The closest answer choice, without rounding, would be option D: 5.0 m/s², which seems to be a rounding error. The correct centripetal acceleration is approximately 0.559 m/s², which may indicate the multiple-choice answers have a mistake or that there has been a misunderstanding of the question's parameters.