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I understand that the moon causes a tidal bulge on Earth, and this tidal bulge moves slightly ahead of the moon due to Earth's rotation.

When reading about why the moon is moving away from the Earth, the most common explanation given is that the tidal bulge slows Earth's rotation and the moon must speed up due to the conservation of angular momentum. This is a poorly worded explanation as it completely skips the part about what is the mechanism of angular momentum transfer. It assumes that we defined a law and the universe must follow it. No, we found that momentum is always conserved in nature, and we noted it as a law.

Upon digging further, I found the most common explanation for the mechanism of angular momentum transfer is that the tidal bulge exerts a gravitational pull on the moon and speeds it up.

The question that is driving me crazy is that higher orbits are supposed to be slower, not faster. If the moon is speeding up, it should fall closer to Earth rather than move away. The moon must be slowing down if it is moving away from Earth, gaining gravitational potential energy and losing kinetic energy. What am I missing here?

How does the transfer of angular momentum lead to reducing kinetic energy and gaining potential energy? What is the mechanism of action here to cause this?

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    $\begingroup$ This will probably seem bizarre to you now, but in modern theoretical physics conserved quantities are treated as more basic than forces. This is especially true for energy and momentum, where we would rather assume some totally undiscovered force or particle than believe in even a tiny failure of conservation. If we didn't know that there was a tidal bulge, but we did know the Moon was moving slowly away from the Earth, astronomers would say "momentum conservation says there must be a force, we just haven't found it". Another good example is the discovery of neutrinos. $\endgroup$
    – zwol
    Commented Feb 18 at 15:03
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    $\begingroup$ "It assumes that we defined a law and the universe must follow it." No, it implies that the law is an accurate representation of how the universe works, and it then strongly suggests that understanding the law inherently leads to understanding how the universe works. You're not wrong that the correctness of the explanation hinges on the correctness of the law, but your conclusion is decidedly more cynical than how we use laws to explain how the universe behaves. The only alternative would be to not refer to the law and build the explanation from scratch. That would be reinventing the wheel $\endgroup$
    – Flater
    Commented Feb 19 at 0:50
  • $\begingroup$ "The question that is driving me crazy is that higher orbits are supposed to be slower, not faster." I can return a response similar to your "law before behavior" inversion. You are assuming that the orbit prescribes the velocity. No, we found that the momentum is inherent to the object itself, and only in combination with its current location (relative to the body which exerts a gravitational effect on it) defines the orbit. $\endgroup$
    – Flater
    Commented Feb 19 at 0:58
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    $\begingroup$ Note that in "higher orbits are supposed to be slower, not faster" there is a subtle error. A stable circular orbit at a larger radius is slower than a stable circular orbit at a lower radius, yes. But when you're imagining the moon speeding up, you're not comparing its orbital speed at 2 different heights, you're comparing resulting trajectories starting from a given height at two different speeds (i.e. with and without the acceleration). If you're in a circular orbit at a given height and you speed up, your height will start to increase, not decrease. $\endgroup$
    – Ben
    Commented Feb 19 at 3:17
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    $\begingroup$ The apparent contradiction that you have to go faster in order to get into a slower orbit has confused a great many people including astronauts and rocket scientists. :) There are lots of resources available on youtube to explain this, but frankly I did not understand it at any sort of intuitive level until I played Kerbal Space Program for a few days, and now it just seems like the most natural thing in the world. See also xkcd.com/1356 $\endgroup$
    – Eric Lippert
    Commented Feb 19 at 21:27

1 Answer 1

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To understand this, let’s start with a simpler example of orbital mechanics. Suppose we have a rocket in a circular orbit that wishes to transfer to a higher circular orbit. This proceeds in the following steps

  1. Burn the engines to accelerate forward. This increases the velocity to be greater than the circular orbital velocity. Thus the rocket is now in an elliptical orbit.

  2. Follow the elliptical orbit halfway around, to its highest point. Kinetic energy has converted to potential energy and the rocket is higher than the previous orbit and traveling slower than the circular orbit at this higher altitude.

  3. Burn the engines to accelerate forward again. This increases the velocity to be equal to the circular orbital at the new altitude. This new circular orbital velocity is smaller than the velocity for the lower circular orbit.

Note, the rocket accelerates forward both times, and yet ends up traveling slower at the higher altitude. The KE gained by the burns plus some of the original KE is changed to potential energy by gravity.

Now, with the moon, the tidal bulge leads the moon. So the moon is gravitationally attracted to a point slightly ahead of the center of the earth. This attraction can be decomposed into a component toward the center and a component forward.

This forward component acts like the rocket burn. It increases the KE, and as the moon moves up the KE is converted to potential energy. The net result being, as before, a propulsive force acting only forward, but a transition to a higher and slower orbit.

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    $\begingroup$ Wow, this made a whole lot of sense the way you explained it with the rocket example. Thank you! As the "fuel burn" in the case of the moon is continuous would it be right to say the moon is "spiraling" outward from earth, its orbit increasing in altitude every moment? $\endgroup$
    – WillowRook
    Commented Feb 17 at 17:30
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    $\begingroup$ @WillowRook yes, very slowly spiraling out $\endgroup$
    – Dale
    Commented Feb 17 at 21:33
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    $\begingroup$ @WillowRook The tidal bulge effect is very small & slow-acting. The Moon's altitude isn't slowly increasing in a simple spiral pattern. The Moon's trajectory around the Earth-Moon barycentre is approximately elliptical (with eccentricity ~= 0.055). The Moon's orbit is actually quite complicated, mostly because of the Sun. I have some details here: astronomy.stackexchange.com/a/55112/16685 $\endgroup$
    – PM 2Ring
    Commented Feb 19 at 5:02
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    $\begingroup$ Pardon my ignorance, I was just passing by through the hot network links. But, with the hole for every action there is an equal and opposite reaction. Would the earth not also be spending energy maintaining the opposite pull from the moon of which is propelling it? Like in super ape brain terms. +1 moon energy, -1 earth energy? Where is that difference being made up for on the cosmic level? <3 Thanks $\endgroup$
    – jjonesdesign
    Commented Feb 19 at 7:16
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    $\begingroup$ @jjonesdesign Well spotted. The Earth's angular momentum of rotation is being transferred to the Moon, so the day is gradually getting longer. See en.wikipedia.org/wiki/Earth%27s_rotation The Earth's rotation is closely monitored by the International Earth Rotation and Reference Systems Service, who publish regular reports. $\endgroup$
    – PM 2Ring
    Commented Feb 19 at 10:47

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