# Radious of the geosynchronous ORBIT

• 8parks11
In summary, the radius of a geosynchronous orbit for a communications relay satellite is determined by the height from the center of the Earth and the angular velocity. The specific location above the Earth's surface is not as important as the orbit itself. The orbit must be circular and the satellite must experience a centripetal force equal to the gravitational force of the Earth. The radius can be calculated by equating the centripetal force and the gravitational attractive force.
8parks11
a)

What is the radius of the orbit of a communications relay satellite that always reamins above one point on the Earth's surface? Such an orbit is called a geosynchronous orbit.

- I could find this on google but what is an another way to solve this?

b) Can such a satellite be placed in geosynchronous orbit over ANY point on Earth's surface? WHY?

You can find it out by calculating it really. Are you sure that is the only important point? Radius is simply the height from the centre of the Earth and you can have almost any radius you want. What is important is angular velocity.
(Hint: How long does it take fo the Earth to make 1 full rotation?)

b) Yes and no really. The point is not as important as the actual orbit itself.

We assume that the satellite is in a circular orbit. This means that it is experiencing a centripetal force $$F_C$$ supplied by the gravitational attractive force $$F_G$$ of the earth

$$F_C = F_G$$

the centripetal force is given by

$$F_C = m\frac{v^2}{r}$$

with the mass and orbital speed of the satellite. r is its distance from the centre of the earth. The gravitational attractive force is given by

$$F_G = G \frac{Mm}{r^2}$$

## 1. What is the definition of the geosynchronous orbit?

The geosynchronous orbit is an orbit around Earth with an orbital period that matches Earth's rotation period. This results in the satellite appearing to remain in a fixed position in the sky as seen from Earth.

## 2. What is the difference between geosynchronous and geostationary orbit?

Geosynchronous orbit refers to any orbit with a period that matches Earth's rotation period, while geostationary orbit specifically refers to an orbit directly above the equator with a period of 24 hours, resulting in a stationary position relative to Earth's rotation.

## 3. What is the radius of the geosynchronous orbit?

The radius of the geosynchronous orbit is approximately 42,164 kilometers from the center of Earth.

## 4. How is the radius of the geosynchronous orbit calculated?

The radius of the geosynchronous orbit is calculated using the formula r = (G x M x T^2 / 4π^2)^(1/3), where G is the gravitational constant, M is the mass of Earth, and T is the orbital period in seconds.

## 5. What are the main uses of the geosynchronous orbit?

The geosynchronous orbit is primarily used for communication and navigation satellites, as well as weather and Earth observation satellites. It is also used for some space telescopes and other scientific instruments.

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