# Velocity of a satellite in a eccentric orbit

• farolero
In summary, the speed of the satellite at the closest part of the orbit at 100 km is 2 m/s, given that the speed at the farthest part is 1 m/s and the distances are measured to the center of the planet. Conservation of angular momentum was used to determine this speed, which is double the speed at the farthest part due to the halving of the orbit radius.
farolero

## Homework Statement

A satellite is orbiting an still planet, the farthest part of the orbit is at 200 km and the closest part at 100 km.

what would be the speed of the satellite at the closest part of the orbit at 100 km if the speed at the farthest part is 1 m/s?

L=mvr

## The Attempt at a Solution

I tried to apply conservation of momentum with which the result would be 0.5 m/s but I am not sure if this result is valid for its posible the planet acquires a rotation to keep conservation of momentum true, value I dot know how to obtain.

I was told to post this here though is not actually homework, I am already an engineer and finished already my studies but I still want to learn more

farolero said:

## Homework Statement

A satellite is orbiting an still planet, the farthest part of the orbit is at 200 km and the closest part at 100 km.
Are the given distances meant to be orbit radii or heights above the planet surface? It must be a very small planet if they are orbit radii!

If they are heights above the surface then you will need additional information to establish either the true orbit radii (so, the radius of the planet) or the mass of the planet
what would be the speed of the satellite at the closest part of the orbit at 100 km if the speed at the farthest part is 1 m/s?

L=mvr

## The Attempt at a Solution

I tried to apply conservation of momentum with which the result would be 0.5 m/s but I am not sure if this result is valid for its posible the planet acquires a rotation to keep conservation of momentum true, value I dot know how to obtain.

I was told to post this here though is not actually homework, I am already an engineer and finished already my studies but I still want to learn more
Conservation of angular momentum is a good approach, but as mentioned above you need a bit more information about the orbit to fix its size.

As it gets closer the speed increases so 0.5 m/s cannot be th right answer in any case.
But unless you specify what these distances mean, as suggested already, the only thing you can say is that the speed will be larger than 1 m/s.

The distances are to the center of the planet, I suppose the planet has such a mass as to make the farthest orbit data posible

My apologies I am a bit dislexic i meant 2 m/s where i said 0.5 m/s

Notice the radius halves which helps a lot in the calculations.

When the satellite is at 150 km from the planets center, what is the component of its velocity at right angles to a line drawn from the planet's center?

thanks i found the solution to keep angular momentum true it would be 2 m/s

## 1. What is the velocity of a satellite in an eccentric orbit?

The velocity of a satellite in an eccentric orbit refers to the speed at which the satellite is moving as it revolves around a central body, such as a planet or star. It is affected by the mass of the central body, the distance from the central body, and the shape of the orbit.

## 2. How is the velocity of a satellite in an eccentric orbit calculated?

The velocity of a satellite in an eccentric orbit can be calculated using the equation v = √(GM(2/r - 1/a)), where G is the universal gravitational constant, M is the mass of the central body, r is the distance from the central body, and a is the semi-major axis of the orbit.

## 3. Does the velocity of a satellite in an eccentric orbit change?

Yes, the velocity of a satellite in an eccentric orbit changes as the satellite moves along its orbit. It is fastest at the perigee (closest point to the central body) and slowest at the apogee (farthest point from the central body).

## 4. How does the eccentricity of an orbit affect the velocity of a satellite?

The eccentricity of an orbit, which describes how elongated or circular the orbit is, has a direct impact on the velocity of a satellite. A highly eccentric orbit will result in a greater difference in velocity between perigee and apogee, while a circular orbit will have a more consistent velocity throughout the orbit.

## 5. What are some factors that can influence the velocity of a satellite in an eccentric orbit?

Aside from the mass of the central body and the distance from it, other factors that can influence the velocity of a satellite in an eccentric orbit include the gravitational pull of other bodies, atmospheric drag, and solar radiation pressure.

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