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I'm closely following NASA's Artemis 1 mission and all the broadcasts. This week the return powered flyby burn took place, the Orion spacecraft flew around the moon and started its way back home.

Since I don't have a M.Sc. in orbital mechanics, a dumb question came to my mind: before the loss of signal and burn, Orion had a velocity of 4842 mph (see here in the NASA's broadcast before the burn). But after the burn Orion travels with a velocity of 2472 mph (see here in the NASA's broadcast after the burn).

I naively assumed that Orion uses this maneuver to gain speed from the Moon's gravitational force and therefore should be faster afterwards.

Where is my faulty reasoning?

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    $\begingroup$ What frame of reference are the velocities (really speeds) given in? $\endgroup$
    – Organic Marble
    Dec 10, 2022 at 16:08
  • $\begingroup$ Oh, no idea, shall I ask NASA? :) $\endgroup$
    – mu88
    Dec 10, 2022 at 16:19

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Look at the animation of the mission in the Wikipedia article, in particular the one described as "Earth-centered inertial reference frame".

animation

You can see that the initial flyby added a lot of velocity to the spacecraft, and turned its path almost 90°. The second flyby effectively reversed these changes, cancelling all of that "forward" (in the same direction as the Moon) velocity and allowing the spacecraft to begin falling inward toward Earth.

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  • $\begingroup$ That's interesting, thank you! And how does this relate to what I see in the two video sequences? $\endgroup$
    – mu88
    Dec 11, 2022 at 13:10
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Answer: there is no fault to your reasoning. The apparent contradiction comes from a switch in frame of reference from Earth to moon. The Moon’s orbital speed is about 1 km/sec. This may be added to the satellite’s Lunar orbital speed (in an Earth reference plane) or not (in a Lunar reference frame)

For a physicist, there is no place in the universe which is “at rest”, so all motion must be defined in relation to something else. You may feel “at rest” in your Lazy-Boy because you are not moving in relation to the Earth, but the Earth is rotating and also orbiting around the sun and so on.

On its transit to the Moon, Orion is in an eccentric orbit around the Earth, so the News Channel gives its speed in relation to the Earth. Once Orion goes into orbit around the Moon, its speed is reported in relation to the Moon. The description switches back to the Earth frame of reference on the transit home.

Some of this apparent contradiction is confusion between “speed” and “velocity”. In day-to-day usage, they are synonymous. But “speed” is scalar (a one-dimensional number) whereas “velocity” is a vector (location, direction and length).

For instance, in a circular orbit, a satellite has a constant speed but its velocity is always changing. To confuse matters further, if the satellite is orbiting the Moon but if you are describing its motion from the Earth’s frame of reference, the satellite is speeding up and slowing down. This is because its speed is added (or subtracted) from the Moon’s orbital speed depending on where the satellite is in its orbit.

enter image description here

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    $\begingroup$ Do you have a source showing that the two speeds quoted in the question are indeed in different frames of reference? Since your answer is based on that assertion. "The apparent contradiction comes from a switch in frame of reference from Earth to moon." $\endgroup$
    – Organic Marble
    Dec 11, 2022 at 23:42

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