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 Author Topic: The Apollo "Free-Return" trajectory  (Read 2989 times)
bertog
Full Member

Posts: 30

 « on: February 27, 2007, 04:04:03 AM »

Hi All,

I've this question ...

Why the Apollo's "Free-Return" trajectory was in a 8 shape ?

Thanks

Guido
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<< Hey, there it is ! There it is !! Son of a gun, right down the middle of the road !! >> - Pete Conrad
DrLaufbahn
Full Member

Posts: 43

 « Reply #1 on: February 27, 2007, 07:20:15 AM »

First, picture the highly elliptical orbit into which the Apollo spacecraft was injected by the third stage of the Saturn V, an orbit with a perigee of about 180 km and an apogee of something like 400,000 km.  If it weren't for the moon, the spacecraft would have simply orbited the Earth along this very elongated ellipse.  However, the departure from low Earth orbit was timed so that the spacecraft would pass just in front of the Moon.  Imagine looking down on the Earth-Moon system from above the Earth's north pole.  Suppose that the Moon is at 3 o'clock just when Apollo reaches the Moon's orbit.  The Moon is moving counter-clockwise along its orbit at about 1 km/s.  Apollo, having lost most of its kinetic energy on the long coast out from low Earth orbit, is moving very slowly.

Let's imagine that Apollo has just gone slightly past the Moon.  Imagine now that you're moving along with the Moon, looking down from above its north pole.  Then what you see is Apollo approaching the Moon in a clockwise direction on a hyperbolic (open) orbit.   As Apollo gets closer to the Moon, it speeds up.  If Apollo's trajectory has been set up just right, it will pass close to the Moon's far side, curve around the Moon and escape again more or less in the direction of Earth.

Now go back to looking down from above the Earth's north pole.  In this frame of reference, the Moon is once again moving counter-clockwise at about 1 km/s.  Since Apollo is moving more or less toward Earth in the Moon's reference frame (as we saw in the previous paragraph), in the Earth's frame its motion is a combination of toward Earth and counter-clockwise around the Earth.  This is the return leg of the famous figure-8 trajectory.
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bertog
Full Member

Posts: 30

 « Reply #2 on: February 27, 2007, 12:20:53 PM »

Good explanation  Thank you very much
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<< Hey, there it is ! There it is !! Son of a gun, right down the middle of the road !! >> - Pete Conrad
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