Eli5: how does the James webb telescope orbit relate to the three body problem ..

Question

An article I read said we haven’t solved the three body problem and can’t predict the motion of 3 orbiting things in motion (2002 VE “Venus moon”) but we’ve been able to get the telescope to orbit just fine with itself the earth and the sun.. what’s the difference?

In: Physics

Answer 1

The 3-body problem is there is no general closed-form solution to where an object will be in the future.

That means there is not an expression you can just input the time in the future and directly get into what position the object will be. I you travel i a straight line at 7 m/s the distance you are along the into at time t is 7*t. So if I calculate where you are in 564 seconds the answer is 7* 564=3948m away from you at time 0.

You can create a formula like that for the orbit of two objects. It will be larger but you can just input the time

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For three bodies you need to do a calculation like how will the object move in 1 second, then use the new position and calculate for the next second. The accuracy will depend on the length of steps but also the precision of the number you have in the computation. If the calculation just has 10 decimals you can’t have time steps that only change the 11th decimal. Smaller steps also mean more steps and a longer time to calculate the result.

Even for two bodies in practice, we will not know the exact future position. You need to know the distance exactly and the mass. All real-world measurements have a margin of error.

For the James Webb Space Telescope, we can calculate where it will be with high enough accuracy to know where it should be placed. We can then measure where it is and use the trust to keep it in the required orbit.

Even if we could calculate it all exactly we would not know exactly where it will be. Light and the solar wind result in a force in the spacecraft. How large depends on the exact orientation of the spacecraft. We do not know exactly where it will point and for how long. The exact strength of the solar wind is also not known in advance.

So in practice, all calculated result has a margin of error because we can measure all input variables exactly enough. In addition some parameter are not constant and will change.