"Geosynchronous" means "simultaneous with the Earth". A geosynchronous satellite is one which rotates about the Earth's axis at the same speed as the Earth itself revolves.
The speed at which an object orbits the Earth depends on its distance from the Earth. An object close to the Earth must move very quickly to remain in orbit and avoid falling to the Earth, while an object far away from the Earth feels very little gravitational attraction and must move very slowly to avoid flying out of orbit away from the Earth. Somewhere in between, at an orbital height of about 23,000 miles, the orbital speed of an object just happens to coincide with the rotation speed of the Earth, so that one orbit takes exactly 24 hours. An object at that distance in orbit over the Equator remains directly over the same spot on the Earth permanently.
Although not to scale, the animation below illustrates this principle. Notice that the satellite orbits at exactly the same speed as the Earth is rotating, so that it is always located off the coast of the Americas.
Usually, the United States has two geosynchronous satellites in orbit at all times: one over the East Coast and one over the West Coast. In addition, other countries or groups of countries, such as Europe, India, and Japan, have their own geosynchronous satellites. Together, these satellites provide almost complete coverage of the Earth, except for polar regions where the angle of view is poor.
A second type of weather satellite orbit is called a polar orbit, shown in the animation below. Typically, these orbits are much closer to the Earth, so that the satellite travels rapidly over the Earth's surface. True to the name, each orbit takes the satellite over the North and South Polar regions. Often the orbits are lined up with the Sun so that the satellite passes over different spots on the Earth at the same time of day. The close proximity to the Earth is a tradeoff: much greater detail is visible, but an image might be available for a particular location only one to four times a day. Because of their infrequency, these satellites are not as commonly used in weather forecasting.
Question: Why must satellites in lower orbit move faster to stay in orbit?