How long would it take two planets to collide?

[rohanlol7]

So, i was on the plane going for oxford interviews and i was thinking about what i could be asked. While i was thinking i came up with this one. Suppose the Earth and the moon were at a distance α apart at rest, how long would it take for them to crash into each other. I'm only really considering an ideal situation where the system is only comprised of the Earth and the moon. So i tried to solve it in general for two planets of mass M1 and M2 respectively.
If anyone could provide a method or a solution. I was initially going to type in my work but its going to take hours. if anyone wants to see it just pm me. ( mine involves conservation of energy and momentum and len gthy calculus. my solution is not complete as the function i obtained was so complex that i was too lazy to substitute everything in. thanks everyone

 

[Bystander]

End of collision is cessation of interaction? As in attractive force, but no longer permanent distortions?

 

[rohanlol7]

Hmm I don't know actually. I just took them as point masses. Does it actually matter what happens at the collision when I'm trying to find the time taken for them to impact?
If I'm making no sense I probably misunderstood you

 

[A.T.]

http://physics.stackexchange.com/qu...-masses-will-collide-due-to-Newtonian-gravity
https://www.physicsforums.com/threads/time-for-two-bodies-to-collide-under-gravity.246833/
https://www.physicsforums.com/threads/time-for-two-point-masses-to-collide-under-gravity.523762/

 

[rohanlol7]

Thanks

http://physics.stackexchange.com/qu...-masses-will-collide-due-to-Newtonian-gravity
https://www.physicsforums.com/threads/time-for-two-bodies-to-collide-under-gravity.246833/
https://www.physicsforums.com/threads/time-for-two-point-masses-to-collide-under-gravity.523762/

:)

 

[russ_watters]

What I've always found interesting about this - if I remember correctly - is that for the first day you wouldn't even notice unless you were really paying attention.

 

[rohanlol7]

Notice what? :D

 

[russ_watters]

Notice what? :D

The moon careening toward Earth.

 

[phinds]

The moon careening toward Earth.

Right. On the first day it would be more like "looking in that general direction" rather that "careening towards"

 

[anorlunda]

What would be fun would be to see a real time animation of Theia colliding with Earth to form the moon.

 

[rohanlol7]

Ah i never thought of that. I would love to see one where the Earth slowly spirals towards the sun for some sort of reason

 

[Janus]

What I've always found interesting about this - if I remember correctly - is that for the first day you wouldn't even notice unless you were really paying attention.

I assume that you mean that if the Moon were falling straight towards the Earth, you wouldn't see a noticeable increase in its size for the first 24 hrs. This is likely true, as in the first 24 hrs, its angular size would only increase by ~3%. And assuming that it started at it's average distance, it would not even have reached its normal perigee distance yet. In the next 24 hrs, it will increase by another 9.5% for a total increase of 12.5%, which should be noticeable (but maybe not to the casual observer. the Moon in its semi-monthly trip from apogee to perigee changes size by ~17%*, so I wonder if someone not looking for it would notice a 9.5% increase in size between two successive nights, since the Moon would still be within its normal range of viewing size.)
12 hrs later, it will have swollen another 9.5% and be 22% larger than it started, and 12 hrs later than that it will have grown to 36% larger than what it started at, and somewhere by now people will begin to notice. * as an aside, if the Moon started falling at apogee, it would take a little over 2 days to fall to its normal perigee distance.

 

[A.T.]

Right. On the first day it would be more like "looking in that general direction" rather that "careening towards"

http://cdn2-b.examiner.com/sites/default/files/styles/image_content_width_large/hash/c1/25/c125eeaea3694b51520ec74710f6f5cc.jpg?itok=CXgs-OJv

 

[mfb]

Lunar laser ranging would note it within seconds (assuming they do a measurement at the right time):
- they would not hit the retroreflectors any more due to the lack of lateral motion.
- if the moon does not happen to be at its highest point in the sky, the radial distance would become different as well. This can be noted with the first light pulse even after fractions of a second - but this light pulse takes ~1.5 seconds to reach the station. And that is really the absolute limit on notability speed.

 

[Janus]

Lunar laser ranging would note it within seconds (assuming they do a measurement at the right time):
- they would not hit the retroreflectors any more due to the lack of lateral motion.
- if the moon does not happen to be at its highest point in the sky, the radial distance would become different as well. This can be noted with the first light pulse even after fractions of a second - but this light pulse takes ~1.5 seconds to reach the station. And that is really the absolute limit on notability speed.

It also wouldn't take any amateur astronomer too long to note that the Moon was no longer moving relative to the background stars, since this motion is about its angular size per hour.