# Angular Momentum in a Kepler Orbit

1. May 6, 2013

### Rapidrain

I got myself here a satellite rotating at a large distance around planet X.

Distance from center of planet X = 100,
mass of the satellite = 1 gram (really small),
mass of planet X = 1.0 kg
velocity of my satellite 10 m/sec
and in this oddball universe the gravitational constant = 10**4

So the satellite-planet X system has an angular momentum of 100 * 10 = 1000 m**2/sec

Now suddenly I place a second planet, planet Y, right next to planet X

mass of planet Y = 1 kg

So at this instant, the central gravitational source is now 2.0 kg but distance is still 100 and velocity of satellite is still 10

My question : has the angular momentum of the system increased?

I'd like to use angular momentum conservation to figure the characteristics of a
satellite / planet / planet trajectory. That's where I'm going with this.

2. May 6, 2013

### tiny-tim

Hi Rapidrain!
Angular momentum = radius "cross" momentum.

Neither the momentum nor the radius has changed, so the angular momentum is also the same.

The satellite will follow an ellipse instead of its original circle.

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