High School How to calculate the energy released?

[kinchit bihani]

TL;DR

I was wondering if anyone could guide me in calculating how much energy would be released when the following phenomenon happens: the earth stops in its tracks and rolls down the space time curve to hit the sun.

Would Earth's moon also collapse into the Sun? In that case, how much energy will be released with that collision too? How will it compare it with the earth-sun collision?

Is there a possibility of this situation arising in the lifetime of earth?Thanks in advance.

 

[anorlunda]

Temporarily closed for moderation.

 

[Nugatory]

I was wondering if anyone could guide me in calculating how much energy would be released when the following phenomenon happens: the Earth stops in its tracks and rolls down the space time curve to hit the sun.

If we were to stop the Earth in its tracks (we’ll assume that by this you mean “bring the Earth to rest relative to the sun”) it would fall straight down into the sun for the same reason that when you hold a ball at rest relative to the surface of the Earth and then let go, it falls straight down towards the surface of the earth. (But do note that that it’s somewhere between very misleading and just plain wrong to describe this as “rolling down the spacetime curve” - that’s not how curvature produces gravitational effects).

In principle we would calculate the energy the same way too: integrate the force $Gm_Em_S/r^2$ over the distance covered by the falling earth. (There are simplifications available for the dropped ball, and in practice we would use them to avoid the integral).

Would Earth's moon also collapse into the Sun?

No. From an earth-centric point of view the moon goes in circles around the earth, but if you look at things from a sun-centric point of view you’ll see that the moon is orbiting the sun on an undulating path that puts it alternately inside the earth’s orbit and outside.

Is there a possibility of this situation arising in the lifetime of earth?

No. There is nothing out there that culd conceivably slow the Earth that much.

 

[sophiecentaur]

how much energy would be released when . . . . . . . . .the Earth stops in its tracks and rolls down the space time curve to hit the sun.

This thread was examined by the Mods because Physics doesn't usually consider the result of things 'just happening'. A proper question should include how you get the stopping to happen in the first place.
You have to remember that the Moon has both Gravitational Potential Energy (you refer to this) and Kinetic Energy (it's moving). The amount of KE is actually half the PE (for a circular orbit) so 'stopping' the Moon in its orbit would require all that KE and that would have to come from somewhere.
To make a spacecraft land on Earth, you have to do just that but the atmosphere helps a lot because, once your engines have brought the craft down to a level where the atmosphere is thick enough, the energy is dissipated as heat, due to friction. Alas, the atmosphere wouldn't have significant effect on the massive Moon so you would have to provide pretty well all of that energy (to 'subtract' the KE). What sort of a rocket (including the fuel) would you imagine that could do that job? A pretty crazy idea, aamof.

Here's something to think about: the Earth spins once a day and the Moon goes round once a month. The two bodies are not perfect spheres and the Earth's rotation is slowing down a very tiny amount due to gravitational interaction AND the Moon's orbit is being pulled along (a bit) in its orbit. So the orbit of the Moon is increasing every year by about 38mm. The energy for that comes from slowing the Earth's rotation down a bit. Eventually they will be both facing each other all the time! That shows you just how much Energy requirement is required for that thought experiment that came into your head.