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1

Let's look at what happens if we put numbers into your equations to see if there actually is a violation of the conservation of energy. Using numbers for Earth from wikipedia we have a velocity of $29.78*10^3\frac{m}{s}$ for orbital velocity and a mass of $5.972*10^{24}kg$. For say the Voyager 2 we have mass of about 730 kg and a speed of ...

1

I read that the KE a free-falling ball acquires is not originated by the attracting body but that energy was actually stored in the ball when it had been lifted to the height it dropped from. In this way, it was said, gravity is subject to the conservation of energy principle and cannot change the total energy of an object. Consider now the ...

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Energy is in fact conserved, even in gravitational slingshots. After the slingshot, the velocity of the spacecraft may indeed change, which means its kinetic energy will also change. If this happens, the energy increase (or decrease) will be made up by a commensurate decrease (or increase) in the kinetic energy of the planet. In plain English: The planet ...

84

Cory, here's a different way of thinking about gravity assists that may help: First is my short answer for readers in a hurry: What is really going on is a giant game of pool, with fast-moving planets acting as massive cue balls that impart some of their energy when they whack into tiny spacecraft. Since you can't bounce a spacecraft directly off the ...

7

Gravity assists don't change speed in the two body problem. An object approaching a lone gravitating body will enter and leave the vicinity of that body with exactly the same speed. All that a lone gravitating body can do is change the direction in which the object is heading. The body that provides the assist needs to be moving with respect to the target ...

4

Because of the practical considerations, we can ignore the relativistic calculations for now. The acceleration of a spacecraft depends on its mass (including unburned fuel it is carrying) and the engine it uses. And the amount of time it can accelerate depends on how much fuel it has. Some of the total consequences of this can be found in the Tsiolkovsky ...

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