What is the minimal velocity boost to bring a satellite down to Earth?

• 2DGamer
In summary, the satellite must be given a negative velocity boost in order to be brought back down to Earth. This boost must be greater than the gravitational acceleration at the surface of the earth, which is about 9.8m/s2.
2DGamer
A satellite is orbiting Earth in a circular orbit of radius R. At some point the satellite has to be returned to Earth and so it is given a sudden negative velocity boost in the direction opposite the satellite's forward velocity). The radius of the Earth is r, and the gravitational acceleration at the surface of the Earth is g. Find the minimal boost required to bring the satellite down. (neglect air resistance).

Ok, this seems pretty straight forward and not too difficult, however it's proving to be quite difficult. I know that initially the satellite is moving in a circular orbit so the eccentricity is zero. But when it slows down the orbit becomes elliptical with the perigee on the surface of the earth. Any help whatsoever will be greatly appreciated! Thanks!

If so, you can then work out what it's orbital velocity is.

And from there, you can then know how much deceleration is required to drop it out of orbit.

That's a fairly simplistic view.

No, I don't know what R is. Just that it's the orbital radius of the satellite. I don't think I'll get an actual number here. Probably an equation that will allow me to plug in any value for R.

Well this sounds like homework so I can't just give you the answer.

As I laid out above, follow that and you will arrive at an answer which would be:

Orbital Velocity must be < Xm/s to drop out of orbit and so an acceleration of at least -Xm/s2 is required must be applied to the orbiting satellite.

The difference is instead of working with numbers, you are simply rearranging the values to give an equation for orbital velocity and from there you know how much to slow it down by.

Last edited:

Sure, I can help with this problem. First, let's define some variables: R is the orbital radius of the satellite, r is the radius of the Earth, and g is the gravitational acceleration at the surface of the Earth.

To find the minimal boost required to bring the satellite down, we need to calculate the final velocity of the satellite when it reaches the surface of the Earth. This can be done using the conservation of energy principle.

Initially, the satellite is in a circular orbit, so its total energy is given by:

E = -GMm/2R

Where G is the gravitational constant, M is the mass of the Earth, and m is the mass of the satellite.

When the satellite is given a sudden negative velocity boost, its total energy will change to:

E' = -GMm/2(R+r) - 1/2mv^2

Where v is the final velocity of the satellite.

Since energy is conserved, we can set these two equations equal to each other and solve for v:

-GMm/2R = -GMm/2(R+r) - 1/2mv^2
GMm/R = GMm/(R+r) + 1/2mv^2
GMm/R - GMm/(R+r) = 1/2mv^2
v = √(2GM/r)

So, the minimal boost required to bring the satellite down is given by the final velocity calculated above. This boost will cause the satellite to have a parabolic orbit with the perigee at the surface of the Earth.

I hope this helps! Let me know if you have any further questions.

1. What is a satellite orbiting Earth?

A satellite orbiting Earth refers to an object that is placed in orbit around the Earth, either by natural means (such as the Moon) or by human technology. Satellites are used for a variety of purposes, including communication, navigation, weather tracking, and scientific research.

2. How do satellites orbit around Earth?

Satellites orbit around Earth due to the combination of their velocity and the gravitational pull of the Earth. They are launched into space at a specific speed and direction so that they can maintain a stable orbit around the Earth. This is known as orbital velocity.

3. What factors affect the orbit of a satellite around Earth?

The orbit of a satellite around Earth is affected by several factors, including the mass and gravity of the Earth, the altitude of the satellite, and any external forces such as atmospheric drag or solar radiation. These factors can cause slight deviations in the satellite's orbit over time.

4. How is the orbit of a satellite monitored and controlled?

The orbit of a satellite is monitored and controlled by ground stations, which use tracking systems and communication devices to communicate with the satellite. If necessary, small rocket thrusters on the satellite can be used to adjust its orbit and keep it in the desired position.

5. What happens to satellites when they reach the end of their lifespan?

When a satellite reaches the end of its lifespan, it can either be deorbited and burned up in the Earth's atmosphere, or it can be moved into a higher orbit to prevent it from becoming space debris. In some cases, satellites may also be repaired or refurbished to extend their lifespan.

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