Can A Satellite Orbit Path Can Be Changed

Long time reader, Fran, asked for a asking and I tin't turn it downwardly. What happens when you lot have a spacecraft that wants to change orbital distances. Do you need to speed up or slow downwardly? Permit'due south begin.

So, I take some spacecraft orbiting a planet - say Earth in a perfectly circular orbit. What must be truthful? Well, I have done this one before, so let me cutting to the chase. The space craft just has i strength on it, the gravitational force. As well, information technology is accelerating considering it is moving in a circle. Here is a diagram.

With just the gravitational force and with a circular acceleration, the following must be true in the management of the eye of the planet (and circle):

I could solve this for the velocity needed for an orbit with radius r - but I won't. Instead let me find the kinetic energy needed for an orbit. Multiplying both sides of that equation be r over 2, I get:

Now for energy. If I consider the satellite (or spacecraft) and the World as the system, then there is no external work on the system so:

The gravitational potential free energy for the Earth-affair organization is:

This gives a total energy for an object in orbit of:

At present let'southward pretend. Suppose we are in orbit at a altitude r ₁ from the centre of the Earth. This means that we would have to have an free energy of:

With a kinetic energy and velocity:

Mission Control at present wants the spacecraft at a lower orbit, say r ₂. Do I need to speed up or ho-hum down? First, what happens to the total alter in energy from E₁ to Eastward_ii?

Since r ₂ is smaller than r ₂, the alter in energy for the system is negative. What does this mean? It means that the piece of work on the system must exist negative. Remember that the work-energy principle says:

The only way to make the work done negative would exist to have a force (in this example from your rockets) in the opposite management as the way you are going. Would your speed increment or decrease? Well, from the speed equation above, I can see that every bit r gets smaller and then (oh, and forgive me for calling 5 the velocity when I am using it every bit a scalar):

So, the change in speed of the spacecraft is positive as it gets closer to the World (since r ₁ is greater than r ₂). This is kind of cool. You are doing negative piece of work on the system, but the kinetic energy increases. It is not as odd as it might seem. Peradventure it is but counter intuitive. But don't forget about the gravitational potential energy. As the spacecraft moves down, the potential free energy decreases. Information technology turns out the potential free energy decreases more than energy needed to orbit. So, if you just "fell" to a lower orbit, you would be going too fast to exist in a round orbit. Maybe this energy graph will help.

I guess you lot just have to expect at two things. The K curve gets bigger, simply the full free energy curve gets smaller. So, you speed up just y'all have to fire your rockets backwards.

Source: https://www.wired.com/2010/11/changing-orbits-and-changing-speed/

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