how exacly are scientists in NASA calculating orbits of their satelites?

Question

For example, lets say NASA wants to send a satelite aroud a moon,

if they want this spacecraft to be in a certain orbit, they need to know at what speed it needs to be moving; how are they going to calculate that speed?

by using Newton’s equations or by using some special relativity equations?

In: 26

Answer 1

Using nth body simulations, you can find if initial velocity in x,y,z will result in a stable orbit rather than fly off into space or crash into earth. A simple program will iterate through time, say by 0.01 seconds per step, the smaller the step, the more accurate the simulation.
From the Gravitational constant*Mass(Earth) * Mass(sat)/Distance^2 = force of gravity you can write it as dV = (dT * G * Mearth)/D^2 by changing dT each step you can update the corresponding dV of each axis add it to the old velocity then update its position.