Find a location where all forces on a satellite cancel each other. The satellite will then rotate with the Earth and the Moon. Click somewhere to place the satellite. Watch what happens. Stop and reset to try again.
Learning aims
In this problem, we are going to work with gravitational fields and their potentials, which are mathematically equivalent to electrostatic fields and their potentials. For a point mass/charge, the gravitational/electrostatic fields fall of with 1/R2, where R is the distance from the point mass/charge. Both are "conservative vector fields", meaning that they can be described as the gradient of a scalar potential (see Feynman volume II, chapter 2 for an introduction of gradients and scalar fields, and Feynman volume II, chapter 4, 4-3, 4-4 for the relation between electric field and electrostatic potential).
Useful resources
The song from the lyrics: David Bowie's Space oddity.
A nice instructional video from Sixty symbols with background information on Lagrange points and their application.
More information on Lagrange points can be found on Wikipedia and elsewhere.
Acknowledgements
This assignment was part of the Fields and Waves course on electrodynamics developed by Michel de Jong and colleagues. The simulation was written by Anjo Anjewierden as part of a 4TU project.
The problem we are dealing with is to find out what could happen to Major Tom, a fictional astronaut. Our only clue are the lyrics of Space Oddity":
So what is Major Tom's fate? How can we find out where he could wind up? Have a look at the picture below, maybe something like that could help us out. How could we make such a picture, and what would it be able to tell us? Could we perhaps find out what forces would act on Major Tom from it, and hence where he would go from a certain point in the picture?
You could use the principle of superposition to determine the force acting on Tom by adding different contributions to the net force. However, you would be adding vectors, which is kind of a tedious exercise. Perhaps there is another way?
Hint: The Earth-Moon system is in motion (it is rotating...). One therefore also has to consider forces other than the gravitational pull of Earth and Moon.
Perhaps you found that Major Tom's most likely fate is to crash into the Moon, but that is not so romantic. Suppose he is still hanging out there, in some kind of perpetual trip. Then it must be somewhere where there are no net forces on him...
The special points where are all forces cancel are called Lagrange points, L1-L5. At which of these points would Major Tom be in a stable position?
Here am I floating round my tin can,
far above the moon
Planet Earth is blue
and there's nothing I can do
Still I am floating in my tin can
on a journey without end
Centrifugal is there too
Kordylewski is what I choose
