Communications satellites are placed in circular orbits where they stay directly over a fixed point on the equator as the earth rotates. These are called geosynchronous orbits. The altitude of a geosynchronous orbit is 3.58 x 10^7 m (approximately 22,00 miles) . Astronomical data are inside the back cover of the book (a) What is the period of a satellite in a geosynchronous orbit?

Verified step by step guidance

1. Understand the concept of a geosynchronous orbit: A geosynchronous orbit is one where the satellite's orbital period matches the Earth's rotational period. This means the satellite will appear to stay in the same position relative to the surface of the Earth.
2. Identify the period of the Earth's rotation: The Earth rotates once every 24 hours, which is equivalent to 86,400 seconds. Since a geosynchronous satellite must have the same rotational period as the Earth, this will also be the orbital period of the satellite.
3. Apply the concept to the satellite: Since the satellite in a geosynchronous orbit must complete one orbit in the same time it takes for the Earth to make one complete rotation, the period of the satellite in a geosynchronous orbit is 24 hours.
4. Convert the period into seconds for calculations in physics, if necessary: Multiply the number of hours in one day by the number of seconds per hour. (24 hours/day * 3600 seconds/hour = 86,400 seconds).
5. Conclude that the period of a satellite in a geosynchronous orbit is 24 hours or 86,400 seconds.

Key Concepts

Geosynchronous Orbit

A geosynchronous orbit is a circular orbit around the Earth where a satellite's orbital period matches the Earth's rotation period, approximately 24 hours. This allows the satellite to remain fixed over a specific point on the equator, making it ideal for communication purposes. The altitude of such an orbit is about 35,786 kilometers (22,236 miles) above sea level.

Orbital Period

The orbital period is the time it takes for a satellite to complete one full orbit around a celestial body. For geosynchronous satellites, this period is equal to the rotational period of the Earth, which is approximately 24 hours. This synchronization ensures that the satellite appears stationary relative to a point on the Earth's surface.

Centripetal Force and Gravity

In a satellite's orbit, centripetal force is required to keep it moving in a circular path, which is provided by the gravitational force exerted by the Earth. The balance between these forces determines the satellite's speed and altitude. For a geosynchronous orbit, the gravitational force must equal the required centripetal force for the satellite to maintain its position relative to the Earth's surface.