Question

A satellite is placed in a geosynchronous orbit. In this equatorial orbit with a period of 24 hours, the satellite hovers over one point on the equator. Which statement is true for a satellite in such an orbit?a. There is a tangential force that helps the satellite keep up with the rotation of the Earth.b. There is no acceleration toward the center of the Earth.c. The force toward the center of the Earth is balanced by a force away from the center of the Earth.d. The satellite is in a state of free fall toward the Earth.e. There is no gravitational force on the satellite.

Answer 1

The true statement about a satellite in a geosynchronous orbit is that it is in a state of free fall toward Earth. It remains in its orbit due to Earth's gravity acting as the centripetal force, and appears to hover over one point on the equator due to its period matching Earth's rotation.

Step-by-step explanation:

For a satellite in a geosynchronous orbit, the correct statement is that the satellite is in a state of free fall toward the Earth. This is because even though the satellite is moving in a circular orbit and does not seem to be falling towards Earth, it is still under the influence of Earth's gravity. This gravitational force acts as the centripetal force necessary to keep the satellite moving in a circular path, allowing it to match the rotation of the Earth and appear stationary above a single point on the equator.

It's important to refute incorrect statements: a is wrong because there is no tangential force other than gravity acting on the satellite; b is incorrect since there is centripetal acceleration toward Earth's center; c is wrong as there's no force pushing the satellite away from Earth—it is gravity that provides the necessary centripetal force; and e is incorrect since gravity is acting on the satellite—indeed, it's integral to the satellite maintaining its orbit.

Answer 2

see that the correct one is D

Step-by-step explanation:

In this problem the satellite is subjected to the universal force of attraction

F = G M m / r²

using Newton's second law with centripetal acceleration you can find the angular velocity of the satellite

F = m a

F = m w² r

G M / r³ = w²

and w = 2π / T

In this case, the satellite is in a two-dimensional movement, where the free fall of the satellite is compensated by the horizontal displacement, for which it is always at a distance from the earth, remaining at the same point.

When reviewing the different statements we see that the correct one isD