/sci/ - Science & Math

Anybody who hates this thread has negative iq points. None of you were involved in making these equations and they were just given to you.

They aren't good and can be improved. What's wrong with stating that?

Fuck off losers.

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.

>>6293400

There, I've worked on it.
Putting it on an integral due to the variable acceleration, I've expanded the newtonian gravitational problem problem to
<span class="math">\int_{0}^{T}dt=-\int_{r_0}^{0}dr\sqrt{\frac{rr_0}{2G(M+m)(r_0-r)}}=\frac{\pi}{2\sqrt{2}}\frac{r_0^{3/2}}{\sqrt{G(M+m)}}[/spoiler]

about 152 seconds over the course of 5 meters.

So /sci/

How do you prove that using Newton's law of universal gravitation you actually get planets orbiting other planets without running a simulation? I mean Newton didn't actually have computers right?

Hai Guise.

I had an interesting question come up in conversation at work today - not related to my work at all tho.

What would be the mass of the largest asteroid that a human could escape under it's own power?

I can begin to see how this would be answered (gravitational force, escape velocity, maximum force produced by a person, etc.) but I thought you guise might find it intredasting too.

F is the force between the masses
G is the gravitational constant
m1 is the first mass
m2 is the second mass
r is the distance between the masses

Thats how it works according to papa Newton.