Explore Tidal Forces in Earth-Moon System

[Vrbic]

Hello,
I'm interested in tidal force of Earth - Moon system. How can I describe this force in lagrangian? I understand it is complex problem, but I'm looking for some kind of toy model or something like that just for my understanding.
What do tidal forces cause? I needn't exact mechanism how, but its consequences on behavior of orbit, period, spin etc.
Thank you for your comments.

 

[Noctisdark]

You can express it usings Newton's law for gravity, F = GMm/r², the tidal forces are difference of forces of gravity btw 2 points, It's easy to calculate, name it F_τ ≈ GMmΔr/r³ then you must the materials that make up the moon to know they elasticity (Young Modulus), Y = F_τ*L₀/(A₀*ΔL), you can know calculate ΔL, I know this doesn't answer your question, but It's impossible (Or very hard, I can't think of a way) to calculate this using lagrangian mechanics, they serve determining equation of motion, there is no "real motion" here unless you redifine elasicity and make a lot of expirements, I've ignored the rotation, I think that GR come up with another method calculating tidal forces using Riemann curvature tensor, but I don't know how, never bumped into this before, Good luck !

 

[Vrbic]

You can express it usings Newton's law for gravity, F = GMm/r², the tidal forces are difference of forces of gravity btw 2 points, It's easy to calculate, name it F_τ ≈ GMmΔr/r³ then you must the materials that make up the moon to know they elasticity (Young Modulus), Y = F_τ*L₀/(A₀*ΔL), you can know calculate ΔL, I know this doesn't answer your question, but It's impossible (Or very hard, I can't think of a way) to calculate this using lagrangian mechanics, they serve determining equation of motion, there is no "real motion" here unless you redifine elasicity and make a lot of expirements, I've ignored the rotation, I think that GR come up with another method calculating tidal forces using Riemann curvature tensor, but I don't know how, never bumped into this before, Good luck !

Wow, interesting, I knew it is complex problem, but I thought you can find some "toy" model version for understundig, but I mean I understand what you want to say. I will continue, I will trying and we will see maybe I will find something comparable with Earth-Moon system.
Thanks for comment, if you have something else (article or idea) please let me know.

 

[russ_watters]

I'm not seeing the problem here. I don't think it is complex at all. Did you not understand how to use the equations Noctisdark provided?

 

[Vrbic]

I'm not seeing the problem here. I don't think it is complex at all. Did you not understand how to use the equations Noctisdark provided?

Hi, no I don't know this equotion, I will google it. For what is it good? Could you tell me more abou procedure etc.?

 

[russ_watters]

Why do you need to google the equation? It is right there in the post. Please rearead post #2, try to make use of the equation and ask a more specific question about the problem you are having with it.

 

[Vrbic]

You can express it usings Newton's law for gravity, F = GMm/r², the tidal forces are difference of forces of gravity btw 2 points, It's easy to calculate, name it F_τ ≈ GMmΔr/r³ then you must the materials that make up the moon to know they elasticity (Young Modulus), Y = F_τ*L₀/(A₀*ΔL), you can know calculate ΔL, I know this doesn't answer your question, but It's impossible (Or very hard, I can't think of a way) to calculate this using lagrangian mechanics, they serve determining equation of motion, there is no "real motion" here unless you redifine elasicity and make a lot of expirements, I've ignored the rotation, I think that GR come up with another method calculating tidal forces using Riemann curvature tensor, but I don't know how, never bumped into this before, Good luck !

Why do you need to google the equation? It is right there in the post. Please rearead post #2, try to make use of the equation and ask a more specific question about the problem you are having with it.

Well, I read all again and I was thinking about that. Noctisdark's idea is nice but I don't know where it is pointing. I'm capable to resolve $\Delta L$ (if I find Young modulus of moon matter) but why? Maybe better (not "super scientific") could be to "guess" functions of orbiting velocities and spins from dissipation of energy due to tidal effects and try to put it to lagrangian. What do you mean?

 

[Noctisdark]

Lagragian are just F = ma in arbitrary co-ordinates, they describe motion, can you express the tidal forces effect on the moon by F = ma ?, If it's possible then you can do it with the lagrangian mechanics, our current definition of elasticity are described by force per mm(sometime m)jusr like hooke's law F = kx th at still hold for some degree to solid materials, then stuff become serious with some tensors, for more information about elasticity check http://physics.info/elasticity/, https://en.m.wikipedia.org/wiki/Elasticity_(physics)

 

[Vrbic]

Lagragian are just F = ma in arbitrary co-ordinates, they describe motion, can you express the tidal forces effect on the moon by F = ma ?, If it's possible then you can do it with the lagrangian mechanics, our current definition of elasticity are described by force per mm(sometime m)jusr like hooke's law F = kx th at still hold for some degree to solid materials, then stuff become serious with some tensors, for more information about elasticity check http://physics.info/elasticity/, https://en.m.wikipedia.org/wiki/Elasticity_(physics)

Thank you, I read it. I also read https://en.wikipedia.org/wiki/Tidal_force where is derived tidal force in the form F=ma.

 

[Noctisdark]

I do not agree with wikipidea on this, F_net = ma not just the force of gravity, and the article describe a tidal force effect, tidal acceleration which explains why the moon gets faster "sometimes",becase tidal forces on Earth make it strech thus make some parts of it (the earth) closer to the moon which will make the moon accelerate more than usual, this can also explain why we see the same side of the moon, other than that, the article don't describe tidal forces, but their effects,

 

[russ_watters]

Well, I read all again and I was thinking about that. Noctisdark's idea is nice but I don't know where it is pointing. I'm capable to resolve $\Delta L$ (if I find Young modulus of moon matter) but why? Maybe better (not "super scientific") could be to "guess" functions of orbiting velocities and spins from dissipation of energy due to tidal effects and try to put it to lagrangian. What do you mean?

I don't understand: You asked the question, so you must decide what it is that you want to know. The equation provided gives the tidal force -- so what, exactly, is the problem you want to solve with it?