ELI5 Tidal acceleration of the moon. Does the mass of the moon affect this?

Submitted by Tegasauras t3_zz9s8q in explainlikeimfive

“Eli5” Tidal acceleration of the moon. Does the mass of the moon affect this?

Hi,

I’ve just started reading up on black holes and, damn this is so interesting but mind boggling so I’m going all way back to understand the basics of gravity that we have knowledge on well enough. I’ve read up ( bought some extra books for references ) but does the mass of our natural satellite affect our tidal acceleration or is it purely based on gravity between that, us and the Sun?

Thank you in advance

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Lithuim t1_j2adeje wrote

The moon’s (or any object’s) gravity is directly proportional to its mass, so yes.

If the moon was a hollow paper mache sphere you wouldn’t get nearly as much tidal effect here on Earth.

The force between the two is G(m1 x m2)/r^2

The moon does exert tidal drag on the Earth, slowly sapping rotational energy and making days longer.

The much more massive Earth has done the same to the moon, dragging it so hard that it’s now permanently fixed with one side facing Earth.

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nekokattt t1_j2afgd8 wrote

(where G is a gravitational constant, 6.67430x10^-11 ; m1 is the mass of the first object; m2 is the mass of the second object; and r is the distance between them, i.e. the radius of the orbit).

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Tegasauras OP t1_j2agbr9 wrote

That makes things much clearer, thank you. Would you be able to point me in a reference of algebra ( let’s start from the basics! ) to start understanding this also?

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Lithuim t1_j2ahfuu wrote

Any middle school algebra textbook I guess. The gravitation equation is thankfully very simple.

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bostwickenator t1_j2adq2e wrote

Gravity is caused by mass so by definition yes. Also acceleration is governed by a=f/m acceleration equals force divided by mass. So it's relevant again there. Is there some other angle you mean here?

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jaa101 t1_j2bjhrg wrote

Adding to the other comments, tidal forces follow an inverse cube law, not an inverse square law. The reason is that they're caused by differences in gravity, not just gravity itself.

As evidence of the cube law, we feel tides from both the moon and the sun, but those due to the moon are about twice as strong. The sun is almost 400 times farther away than the moon but its mass is 27 million times greater, i.e., roughly half of 400^(3).

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