In reference to the below image,

  • The thin black curved line is the Apollo 11 trans-lunar trajectory (outbound)
  • The dark blue line is a tangent to the trajectory just after the TLI burn (as best as I can draw it)
  • The light blue lines represent the straight-line paths between the center of the Earth and the TL trajectory (again, as accurately as I can draw them). In other words, the direction of Earth's gravitation on the spacecraft.
  • The olive-green line is the trans-earth trajectory the spacecraft took (return)
  • The red line is the tangent to just after the trans-earth injection
  • The pink lines are analogues to the light blue lines, but for the trans-earth (return) trajectory

I feel confident explaining that the distinctive curve of the outbound trajectory (the divergence between the black trajectory line and the dark blue line) was caused by Earth's gravitational influence, seeing how the TLI initially put the CSM/LM in a path "offset" from the center of the Earth (light blue lines).

I'm also pretty sure that this image depicts a strictly Earth-centric reference frame, i.e. no barycentric "wobble".

Now, I would assume that the trans-earth trajectory would be a nearly straight line right towards the center of the Earth (i.e. the red line), but based on this diagram, it diverges noticeably.

So, my question is this:

What caused this divergence?

I will suggest a few theories: The change in trajectory was caused by:

  • The force of the solar wind on the CSM (doubtful)
  • Course correction maneuvers (that's a lot of $\Delta v$)
  • barycentric wobble cannot be ignored (or other related perspective factors)
  • The force of the Moon's gravity
  • This diagram just isn't totally accurate

apollo translunar transearth trajectory chart This image was found with a Google image search for "apollo translunar transearth trajectory chart" (with my few modifications) -- as per the notice in the lower left, it is the work of the US Government, and thus public domain.


It takes a few days to get to and from the Moon; since the Moon is orbiting Earth, the Moon's position will change significantly during that time, as marked in the diagram. The curve is caused by the changing direction of the Moon's gravitational pull as it moves.

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    $\begingroup$ I think you may be missing something even simpler. The transfer orbit will have some (initially) transverse as well as (initially) radial momentum, and because the path is nearly straight the Earth's gravity will significantly reduce the latter which leaving the former (mostly) unaffected. $\endgroup$ – dmckee Jun 3 '18 at 17:39
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    $\begingroup$ @dmckee This works for the Earth-to-Moon leg, but what about the Moon-to-Earth leg? The Earth's gravity works to increase the radial momentum in that case. $\endgroup$ – probably_someone Jun 3 '18 at 17:47

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