What is Reddit's opinion of Solar System Dynamics?

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This is not logic this is the mathematics and physics of tidal migration. Please read the text I linked in the previous post as this explains it and comes from published material. You can also read Solar System Dynamics by Murray and Dermott which has the formal mathematics and derivations for tidal migration on page 162 although there is a little work required to then convert to orbital velocities. It is also possible and fairly straight forward to work it out using the Viral Theorem. You can even play with this little toy and see for yourself that increasing the orbital separation results in a reduction of the velocity.

The major problem here is you are trying to think of this in terms of rockets which is not really applicable as the time derivative of the total mechanical energy in such a system is positive while it is negative for tidal migration. You are also neglecting the conservation of angular momentum which constrains the Earth-Moon system.

> By your logic, taking kinetic energy out of the system by decelerating an object gives it more energy by raising its orbit.

This is where you are kind of slipping up and not really understanding tides, which is understandable as they are tricky and subtle. The kinetic energy is converted into gravitational potential energy in an imperfect exchange. I am sure you are aware the Moon has been measured to be migrating away. This means that the gravitational potential energy of the Earth-Moon system is increasing. There is no work being done by an external force and thus the gravitational energy must be coming from somewhere since the total mechanical energy is conserved (with the slight caveat that there is loss due to tidal dissipation). That somewhere is both the reduced rotation of the Earth and the reduced velocity of the Moon.

> The reason I'm saying you've got your logic backwards is that the moon moves slower because of the raised orbit, not the other way around.

These are the same thing. The Moon moves slower because its mean orbital separation is increasing. The Moons mean orbital separation is increasing and so it moves slower. This is simply Keplers laws at play. See for example the mean orbital speed section of this wiki page which has that v_0 is inversely proportional to the root of the orbital separation. So for this expression to maintain its balance if you increase r you decrease v_0.

> Also, an object in a higher orbit has more energy, not less.

This is also somewhat of a problem. An object in a higher orbit has more gravitational potential energy sure. However, if you move an object to a higher orbit without injecting energy it must come at a cost of kinetic energy. This in essence is Virals theorem 1, 2, 3.