# Transferral of orbital energy

1. Oct 19, 2009

### dschmidt12

I know that I have learned this at some point in my past and that I am probably just blanking on the explanation, but I have been having some trouble remembering just how orbital energy is transferred via gravitational encounters (for example, between stars in a binary system). Physically, how is this explained? Also, how does the concept of conservation of angular momentum play into this? Again, I know this is probably simpler than I am making it out to be in my mind; I just wanted to make sure I remembered the reason.

2. Oct 19, 2009

### Bob S

Think first about the Earth-moon system. Moon gravity creates tides and dissipates energy on the Earth. The moon has orbital angular momentum, and the Earth has rotational angular momentum. The only conserved quanty is angular momentum, independent of the rate of energy dissipation.
Bob S

3. Oct 19, 2009

### Cleonis

You use the word 'encounters', which leads me to think you that what you have in mind is the example of gravitational assist, a short duration interaction. (Wikipedia is a good place to start with reading about gravity assist.) Then again, you also mention the case of stars in a binary system, and that's not an encounter, but a continuous interaction; your question is somewhat ambiguous.

Bob S has said some things about tidal interaction, I will say some things about gravitational assist.

Take the case of a space probe, on route to Jupiter, in such a way that on fly-by a gravitational slingshot will take the probe to Saturn.

If you zoom in to a local picture, the probe on a fly-by heading, then to a good approximation the trajectory of the probe is along a hyperbola. Within the scope of that local picture Jupiter and the probe exchange momentum. The direction of motion of the probe is changed by the interaction with Jupiter, and that is reciprocal, the momentum of Jupiter is changed proportionally.

If you zoom out to the scale of Jupiter's orbit you need to take into account that Jupiter and the probe are in individual orbits in the solar system, so angular mechanics applies.

The probe doesn't approach Jupiter "head on", the probe is on a course that makes it "overtake" Jupiter from behind. (Also, Jupiter's orbit is concentric, while the probe's orbit is highly eccentric.)

During the phase of significant gravitational interaction between Jupiter and the probe Jupiter is in a sense "towing" the probe, increasing its orbital energy.

After the fly-by, when the distance between Jupiter and the probe has increased so much that the gravitation between them is negligable compared to the Sun's gravitation their motion can be thought of as individual orbits again. Some of Jupiter's angular momentum has been transferred to the probe, and some orbital energy has been transferred.

Cleonis

4. Oct 19, 2009

### dschmidt12

Yes, I did mean gravitational assist; I'm sorry for being so ambiguous. :) I believe that I understand the concept now, however, I just wanted to make sure that my understanding of the matter was correct. In the case of Jupiter and the probe, during the gravitational force that Jupiter exerts on the probe transfers energy to the probe, thus increasing its velocity by accelerating it. Since angular momentum is also being transferred, the radius of the probe's orbit must also increase, thus changing the orbit of the probe. Thank you so much for all of your help!

5. Oct 19, 2009

### dschmidt12

Ah, thanks, I believe that I understand that now. :)