Yes, you can do this for the Earth and Moon. The moon would start being pulled apart around 9,500km from the Earth, but that is from the centre of Earth. In reality this would happen just over a couple thousand km above the surface.
@XENENEX Yes it would break up at that point. However, it depends on how it approached this limit to whether a ring would be formed or not. If they were moving directly towards each other then it is likely that the material would just fall / collide with the Earth.
how are the eqns for Ft and Fg derived? are they only serving a purpose in this case or do they have a more general application (ie do they apply for ALL objects on the surface of a sattelite orbiting another object?)
They are some what general as it is the gravitational force acting on an object at the surface of the satellite from the satellite and planet. All objects on the surface experience these forces, but if they are not on the closest face of the satellite towards the planet the tidal force will be lower. Physically this means the satellite would be pulled apart from the side facing the planet first, since this is where the tidal forces are strongest
Is Earth considered a rigid or fluid body? I mean if the earth was heading to a black hole, how would it deform before crossing the Roche limit, and what is the factor associated with its rigidity that we would have to use to calculate the Roche limit in such a scenario?
The tidal force is the change in force over some small distance compared to the distance that separates the objects. When the change in distance is small compared the distance r it can be expanded and only the first term is used, the others can be neglected, leaving 2GMur/d^3.
Thank you for the recommendation, I can see how the Roche Limit would have found its way into that book. It is a great way to pull apart planet and moon sized objects.
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Subscribed, There are only a few RUclipsrs like you who do bring the mathematical rigor of Astrophysics, Appreciated the content Thanks!
Thank you, that is great to hear.
Im going to have to start binging from the beginning of these videos to get to catch up lol!!
Thank you. Wonderful explanation 👍👍
Thank you!
Thank you for the nice explanation✌
Beautifully done.
Can you calculate the Roche limit for the earth and the moon?
Yes, you can do this for the Earth and Moon. The moon would start being pulled apart around 9,500km from the Earth, but that is from the centre of Earth. In reality this would happen just over a couple thousand km above the surface.
@@AstroPhil2000 Thank you. This information makes me nervous!
@XENENEX Yes it would break up at that point. However, it depends on how it approached this limit to whether a ring would be formed or not. If they were moving directly towards each other then it is likely that the material would just fall / collide with the Earth.
how are the eqns for Ft and Fg derived? are they only serving a purpose in this case or do they have a more general application (ie do they apply for ALL objects on the surface of a sattelite orbiting another object?)
They are some what general as it is the gravitational force acting on an object at the surface of the satellite from the satellite and planet. All objects on the surface experience these forces, but if they are not on the closest face of the satellite towards the planet the tidal force will be lower. Physically this means the satellite would be pulled apart from the side facing the planet first, since this is where the tidal forces are strongest
Do you have Tidal force formula Derrivation
Do you have a reference for the derivation with the "fluid satellite" ?
Although not a proper reference, this shows how you get the slightly different version for a fluid satellite: en.wikipedia.org/wiki/Roche_limit
Won't the density of both the bodies be more difficult to obtain compared to the other result consisting of radius of the satellite?
Nice one!
Thanks!
Is Earth considered a rigid or fluid body? I mean if the earth was heading to a black hole, how would it deform before crossing the Roche limit, and what is the factor associated with its rigidity that we would have to use to calculate the Roche limit in such a scenario?
Thanku sir 😀
Thank you
Why tidal force is 2GMur/d^3?
The tidal force is the change in force over some small distance compared to the distance that separates the objects. When the change in distance is small compared the distance r it can be expanded and only the first term is used, the others can be neglected, leaving 2GMur/d^3.
Woahhhhhh.....
I came to know about this from a book
WHAT-IF by Randall Munroe
I suggest it to u
It's very interesting....
Give it a read if u can😁
Thank you for the recommendation, I can see how the Roche Limit would have found its way into that book. It is a great way to pull apart planet and moon sized objects.
I am from india