If an artificial earth satellite is in an orbit around the earth’s
equator with a period of exactly 1 day, how does its motion
look to an observer on the rotating earth if it orbits in the same
direction as the earth turns? (Such an orbit is said to be geosynchronous;
most communications satellites are placed in
geosynchronous orbits.)
There is a clear distinction between a geosynchronous orbit and a geostationary orbit. The early recognition of a geostationary orbit was made by the Russian Konstantin Tsiolkovsky early this century. Others referred to the unique orbit in writings about space travel, space stations, and communications. It was probably Arthur C. Clarke who was given the major credit for the use of this orbit for the purpose of worldwide communications.
The geostationary orbit is one where a spacecraft or satellite appears to hover over a fixed point on the Earth's surface. There is only one geostationary orbit in contrast to there being many geosynchronous orbits. What is the difference you ask? A geosycnchronous orbit is one with a period equal to the earth's rotational period, which, contrary to popular belief, is 23hr-56min-4.09sec., not 24 hours. Thus, the required altltude providing this period is ~22,238.64 miles, or ~35,787.875 kilometers. An orbit with this period and altitude can exist at any inclination to the equator but clearly, a satellite in any such orbit with an inclination to the equator, cannot remain over a fixed point on the Earth's surface. On the other hand, a satellite in an orbit in the plane of the earth's equator and with the required altitude and period, does remain fixed over a point on the equator. This equatorial geosynchronous orbit is what is referred to as a geostationary orbit. The orbital velocity of satellites in this orbit is ~10,088.25 feet per second or ~6,877 MPH. The point on the orbit where the circular velocity of the launching rocket reaches 10,088.25 fps, and shuts down, is the point where the separated satellite will remain. The point on the Earth's surface immediately below the satellite is moving with a velocity of 1525.85 ft./sec.
To understand how the motion of a geosynchronous satellite looks to an observer on the rotating Earth, let's break it down step by step:
1. First, let's establish that the observer is stationary on the Earth's surface at a particular location.
2. A geosynchronous satellite is in an orbit around the Earth's equator with a period of exactly 1 day. This means that it takes the satellite exactly 24 hours to complete one orbit around the Earth.
3. Now, consider that the Earth rotates on its axis once every 24 hours as well. This rotation is in the same direction as the satellite's orbit.
4. Since the satellite's orbit and the Earth's rotation period are the same, the satellite appears to remain fixed in the sky from the perspective of an observer on the Earth's surface. It will appear as if the satellite is stationary above a single point on the Earth.
5. This stationary position is especially useful for communications satellites because it allows them to provide continuous coverage over a specific geographic area. This region, where the satellite appears fixed, is referred to as the satellite's "footprint".
So, to summarize, when a geosynchronous satellite orbits in the same direction as the Earth's rotation, an observer on the rotating Earth will perceive the satellite as stationary in the sky, appearing to hover over a fixed location on the Earth's surface. This characteristic makes geosynchronous orbits ideal for applications like satellite television and telecommunications.