# Does an orbiting satellite speed up as it falls towards earth

• LotusTK
In summary, a satellite in orbit around the Earth speeds up as it falls towards Earth due to the conversion of gravitational potential energy to kinetic energy. This is shown by the equation v=sqrt(GM/r), where decreasing r leads to an increase in velocity. Additionally, if a satellite is pushed into a higher orbit without changing its speed, it will eventually spiral away from Earth due to the inability to meet the centripetal force requirement for that particular orbit. Real orbits with atmospheric drag also speed up as their orbit decays, leading to a decrease in velocity and potential reentry. This is due to the conversion of gravitational potential energy to kinetic energy and friction.
LotusTK

## Homework Statement

(sorry for spelling of Earth, had to be to be done to fit it in lol)

Does a satellite in orbit around the Earth speed up as it falls towards Earth?

I understand why the satellite speeds up mathematically. If we equate the centripetal force equation and the equation for gravitational force (because the centripetal force on the satellite is the force of gravity) we end up with

v=sqrt( GM/r)

G = gravitational constant, M = mass of Earth, r= radius of circular motion from centre of earth)

So if you decrease r, v increases, and vice versa.

Is it just simply because the gravitational potential energy of the satellite is being converted into kinetic energy? So instead of just increasing velocity directly towards the Earth like when you drop a ball, its tangential/orbital velocity increases?
I picture the satellite just increasing its velocity directly towards Earth, rather than actually increasing the speed with which it orbits. But then the above formula suggests otherwise.

Also, would i be correct in saying:
If the satellite were to maintain the same orbital speed, but was pushed up into a higher orbit without increasing or decreasing its orbital speed, the satellite will no longer be able to maintain its orbit and begin to spiral away from Earth, because the centripetal force requirement to keep the object in that particular orbit at that particular speed is no longer able to be met by gravity?

Thanks

Without external force and approximating Earth as spherical symmetric mass, the satellite just keeps orbiting in its orbit. If you push it a bit, it goes to a new orbit. No spirals.Real orbits with atmospheric drag speed up as their orbit decays, and it is a simple conversion of gravitational to kinetic energy and heating the atmosphere. At some point drag wins, they get much slower and fall back or burn up rapidly.

mfb said:
Without external force and approximating Earth as spherical symmetric mass, the satellite just keeps orbiting in its orbit.
Real orbits with drag speed up as their orbit decays, and it is a simple conversion of gravitational to kinetic energy and a bit of friction. At some point drag wins, they get much slower and fall back or burn up rapidly.

And is this because of the change of gravitational potential energy to kinetic energy? And when you say speed up, you mean the speed with which it is orbiting, right?

LotusTK said:
And is this because of the change of gravitational potential energy to kinetic energy?
Yes, see the previous post.
LotusTK said:
And when you say speed up, you mean the speed with which it is orbiting, right?
Sure.

LotusTK

## 1. Does an orbiting satellite speed up as it falls towards earth?

Yes, an orbiting satellite does speed up as it falls towards earth. This is due to the acceleration of gravity, which increases as the satellite gets closer to the earth's surface.

## 2. Why does an orbiting satellite speed up as it falls towards earth?

An orbiting satellite speeds up as it falls towards earth because of the acceleration of gravity. The closer an object is to the earth's surface, the stronger the pull of gravity, causing the satellite to accelerate.

## 3. How does the speed of an orbiting satellite change as it falls towards earth?

The speed of an orbiting satellite increases as it falls towards earth. This is because the acceleration of gravity causes the satellite to gain speed as it gets closer to the earth's surface.

## 4. Does the size or shape of an orbiting satellite affect its speed as it falls towards earth?

Yes, the size and shape of an orbiting satellite can affect its speed as it falls towards earth. A larger satellite will experience a stronger pull of gravity, causing it to speed up more than a smaller satellite. Additionally, the shape of the satellite's orbit can also impact its speed.

## 5. Is there a limit to how fast an orbiting satellite can fall towards earth?

Yes, there is a limit to how fast an orbiting satellite can fall towards earth. This is known as the terminal velocity, which is the maximum speed that an object can reach due to the opposing force of air resistance. Once an orbiting satellite reaches its terminal velocity, it will no longer accelerate as it falls towards earth.

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