# Satellite orbiting earth

• Gauss177
In summary, to calculate the height above the Earth's surface that a satellite must be placed to remain over the same geographical point on the equator, you can use the equation v = sqrt(G*m / r), where v is the velocity of the satellite, G is the gravitational constant, m is the mass of the Earth, and r is the distance between the satellite and the center of the Earth. The velocity of the satellite must be equal to the Earth's angular velocity in order for it to remain over the same point on the equator. This means that the satellite must move with the same speed as the Earth's rotation, and therefore the distance r must be greater than the radius of the Earth.

## Homework Statement

Calculate at what height above the Earth's surface a satellite must be placed if it is to remain over the same geographical point on the equator of the earth. What is the velocity of such a satellite?

## Homework Equations

v = sqrt(G*m / r)

## The Attempt at a Solution

At first I thought the velocity of the satellite would have to be the same as the earth, but since r is different the velocity must also be different. I have 2 unknowns for the satellite, the velocity and r, and can't figure out what to do now.

Gauss177 said:
At first I thought the velocity of the satellite would have to be the same as the earth,
It must have the same angular velocity as the earth.

Hm..we haven't covered angular velocity yet. Is there another way to do it?

Whether you've explicitly covered angular velocity or not, there's no way around the fact that if the satellite is to "remain over the same geographical point" its angular speed must equal that of the earth. If you think in terms of both the Earth's surface and the satellite sweeping out equal angles in equal times, that might help you figure it out.

## 1. What is a satellite orbiting Earth?

A satellite orbiting Earth is an artificial object launched into space that revolves around the Earth in a circular or elliptical path. Satellites are used for various purposes such as communication, navigation, weather forecasting, and scientific research.

## 2. How do satellites orbit Earth?

Satellites orbit Earth due to the force of gravity pulling them towards the planet. They are launched at a specific speed and height to maintain a stable orbit around the Earth. The shape and altitude of the orbit can be adjusted to achieve different objectives.

## 3. How many satellites are currently orbiting Earth?

As of 2021, there are over 2,800 active satellites orbiting Earth, with thousands more debris and non-functional satellites. These satellites are owned by various countries, companies, and organizations for different purposes.

## 4. How long do satellites typically stay in orbit?

The lifespan of a satellite depends on its purpose and design. Some satellites have a lifespan of only a few months, while others can last for decades. Factors such as altitude, exposure to radiation, and fuel reserves can also affect a satellite's lifespan.

## 5. How do satellites stay in orbit without falling back to Earth?

Satellites stay in orbit due to the balance between the centrifugal force of their speed and the gravitational pull of Earth. As long as the satellite maintains its speed and altitude, it will continue to orbit the Earth without falling back. If the speed or altitude changes, the orbit may become unstable, causing the satellite to either fall back to Earth or drift away into space.