Okay, guys. Interesting physics question that I made up.
I don't know the solution yet. Consider the following situation. If you want, please submit anything that you want, but don't be idiots. Maybe anything arithmetic, too? Stuff you'd see in highschool textbooks, but problems you'd actually like to solve out.
Here's my problem:
VY Canis Maioris is a very large Hypergiant, and is one of the largest known stars. Pretend it exists a few light years away, and its relative velocity to our solar system is ~+20,000 meters/second initially. Because of the scale, assume that it doesn't matter that they're in angular motion around Sagittarius A*. Assuming that it's approaching the solar system at an angle of 3π/2 rads, assuming that the right hand position is 0 rads or 2π rads.
The solution to this problem is, "At what time will the pull of VY Canis Maioris over power the sun's gravitational pull on the Earth, and cause the Earth to orbit it instead?"
Easy mode: Assume the Earth is remaining still at this time, and for these purposes, it has ZERO rotational velocity; and everything in the solar system doesn't move either.
Normal mode: Assume the Earth has a constant orbital velocity. These will be in the givens below.
Hard Mode: Assume that all the planets start in the same position as well. When will THEY ALL begin to orbit VY CM?
Pretty damn hard mode: Now, factor in the angular movement of them. They are the same as their linear movement.
Note: there are other factors that might affect this like solar wind and shit. You can discount all of it.
>>8156926
Constants/info:
(Law of universal gravitation)
F=(G*m1*m2)/r^2
(Gravitational constant)
G=6.674e-11 nm^2/kg^2
Mass of the Sun: 1.989E+30 Kg
Mass of the earth: 5.92E+24 Kg
Mass of VY Canis Maioris: ~5.96E+31 Kg
Earth's mean distance: 149,597,870,700 meters (1.5E+11 m)
Velocity of Sun: 220,000 m/s (Relative, zero.)
Velocity of VY Canis Maioris: 420,000 m/s. (Relative, 200,000 m/s)
The velocity of Earth: 460 m/s.
Approach angle of VY Canis Maioris: 3π/2 (270°)
θ1 of the Earth: also 3π/2
Mars' v:2.41e+4 m/s
Mars' Mass: 6.42+e23 kg
Mars' mean distance:2.279+e11 m
Jupiter's v: 1.31e+4 m/s
Jupiter's mass:1.90+e27 kg
Jupiter's mean distance: 7.786+e11
Saturn's v: 9.6+e3 m/s
Saturn's mass:5.69+e26 kg
Saturn's mean distance: 1.433+e12 meters
Uranus' v: 6.8e+3 m/s
Uranus' mass:8.68+e25
Uranus' mean distance:2.873e+12 meters
Neptune's v: 5.4+e3 meters/s
Neptune's mass:1.03+e26 kg
Neptune's mean distance:4.495e+12 meters
Mercury's v: 4.74e4 m/s
Mercury's mass:3.3e+23 kg
Mercury's mean distance: 5.79e+10 meters
Venus' v: 3.5e+4 m/s
Venus' mass: 4.87e+24 kg
Venus' mean distance: 1.082e+11 meters
>disregard eccentricity and assume that there is no y component; assume it's 2-d.
>>8156970
Really fuckin difficult mode: Include planetary interaction in this. Oh, god.
>>8156970
Distance to Canis Majoris or gtfo.
>>8156926
Isn't Canis Majoris bigger than most of the solar system, like to the orbit of Jupiter or Saturn? Would Earth even start orbiting the star or just get pulled in and swallowed. Or maybe just flung off into space if we were lucky.
>>8157071
I'm pretty sure I gave that? It's one light year, or 9.4607+e15 meters. This is not an actual estimation, it's only for our purposes.
>>8157084
You said "a few", so that's why I was confused.
>>8157090
My bad, dude. Just use a light year, aka that distance. Damn, I could've sworn i said that.
>>8157090
Also, at that scale, the difference in time for each planet to go into orbit would be insignificant.
Not only that, but the timescales we're dealing with are so enormous that it would be on the order of 10^10 seconds, or about 1000 years. At that point, orbital perturbations would be so severe that it's almost meaningless to approximate.
>>8157100
sounds like a valid answer. Should we change the problem to make it suitable? Like change the star or distance, maybe?
>>8157111
Yeah, probably. But the thing is, since gravity (classically) falls of as r^2, you're gonna have a very narrow window where the problem is actually decently defined. If you want an actually okay answer, you should probably do this in universe sandbox. I don't know if there are really nice analytical solutions for this, since it's gonna be a 3 body problem for each planet; if you try the super hard mode you're not going to have any.
>>8157126
not defined, interesting. Sorry.
>>8157127
Also, I'd say it's very likely that they're all just going to fall into the star, and cause it to start spinning. Angular momentum is conserved, but since there's 0 angular momentum of Canis Majoris w.r.t. Sol, it's just gonna swallow the whole system.
I could estimate the angular velocity of Canis Majoris after collision for you if you want, but not sure how interesting that would be.
>>8157126
I actually have universe sandbox! Maybe I'll upload something.
>>8157152
Sadly you're gonna probably have to scale the problem back a lot- make sure to use RK4 methods and use accuracy speed.
Still won't be super precise, but it'll be ok.
>>8157133
Go ahead! I'm feeling interested.
>>8157408
Sure. The angular momentum of the solar system is about 3.1e43 kg*m^2*s^-1, and the moment of inertia of Canis Maioris is about 2.33e 55, meaning that omega would be about
3.64e-8 + 1.33 e -12 rad/s
(the first term is the already existing angular velocity)
>>8157434
Though that really depends on the orientation of Canis Maioris- it could be opposed to that of the solar system.
It actually doesn't really matter that much.
>>8159130
For what? The questions have been answered.
anyone have similar questions?
