Dual Body Simulation

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Moon V 7 km/s Moon Dist 6380kmkm
Moon Mass = 0
zoom = -0.5

If you worked through the relationship between height and the speed required to maintain an orbit, you may now be wondering what happens as the mass of the satellite becomes significant. When the mass of a satellite is very small compared to a planet that it orbits, the satellite exerts a very small gravitational force on the planet. But the planet exerts a significant graviatational pull on the satellite. However, a body with a significant mass compared to the planet will have a significant pull on the planet. This is something like our Moon and the Earth. The Moon has approximately one sixth of the mass of the Earth and so the Moon will exert a pull of one sixth of the pull that the Earth exerts on the Moon. In addition as the Moon swings around the Earth in its orbit, so to it pulls the Earth around and causes the Earth to wobble. In fact both the Earth and the Moon rotate about the common centre of mass for the two bodies. In this simulation there is a slider for controlling the mass of the satellite (which we now call a moon). The slider controls the fraction of the mass the moon has compared to the planet. So for example a setting of 0.2 sets the moon to be 1/5th (or 20%) that of the planet, and a setting of 1 gives the moon the same mass as the planet.

You can pause the simulation and set the moon to a particular mass and height and launch the moon into orbit and see the effect that a massive moon will have on the orbits of both the earth and the moon.

While you are experimenting with the simulation, you may notice that the behaviour of this simulation is slightly different when the moon crashes into the planet. The planet is rotating and the moon imparts its momentum to the planet causing the wobble to end and the moon will then ride on the plaent in its orbit. We will use this behaviour later to understand the difference between launching in the direction of the rotation of the planet as opposed to launching in the opposite direction to the planet's rotation. Also you will notice that the moon will have to be raised away from the surface of the planet to attain orbit or else it will simply sit on the surface of the planet and rotate with the planet.