Gravity, thou art a heartless b*tch

[D H]

You really do need to start by writing the differential equation.

 

Since you have not done that and since this is not homework, here it is:

 

[math]\frac{d^2x}{dt^2} = \frac{-G(m_1+m_2)}{|x|^3}x[/math]

 

where x is the position of one particle relative to another and m₁ and m₂ are the masses of the two particles.

[Shadow]

Thanks, both of you. DH, could explain the logic behind the equation, or would that be more like asking "Please teach me calculus?" Because the result in itself doesn't interest me that much anymore, it's more the process of getting the result.

[Mr Skeptic]

Thanks, both of you. DH, could explain the logic behind the equation, or would that be more like asking "Please teach me calculus?" Because the result in itself doesn't interest me that much anymore, it's more the process of getting the result.

 

I get a₁=F/m₁, a₂=F/m₂, [math]a=\frac{d^2x}{dt^2}=a_1+a_2=F\frac{m_1+m_2}{m_1m_2}=\frac{-Gm_1m_2}{|x|^2}\frac{x}{|x|}\frac{m_1+m_2}{m_1m_2}=\frac{-G(m_1+m_2)}{|x|^3}x[/math]

 

The point of [math]\frac{x}{|x|}[/math] is to get a unit direction for your force.

[Shadow]

Thanks Mr. Skeptic. It took me a while to understand the process, let alone the reasoning behind it. Do you think you or DH (or anybody for that matter) could post something like a general guideline? Something like "Step 1, write a differential equation...Step 2..." and also the reason for every step...if that wouldn't be too much to ask, I don't know how close this is to a full blown tutorial and how time consuming it would be for the person who writes it. If anyone does so, thanks a million in advance

[swansont]

Differential equations is a class you take after a few semesters of calculus. A "general guideline" would be rather time-intensive

[Shadow]

I meant general guidelines for this specific problem, not differential equations If the why part is the longish one, just leave it out I'm trying to get as much from this as I can without tasking someones time too much.

[swansont]

D H has already pointed out that this is particular problem is rather nasty to solve.

[Shadow]

Okay, I get the hint. Just one last question, would it be possible (I know it'd be insanely hard) but would it be possible to make a gravitational field dependent on time?

[swansont]

Okay, I get the hint. Just one last question, would it be possible (I know it'd be insanely hard) but would it be possible to make a gravitational field dependent on time?

 

You'd have to do it by moving masses around.

[Shadow]

Well yeah, they'd move according to the gravitational acceleration at that point, which would be given by the vector field...I guess it's basically the same problem as this one, only on a broader scale. So it could be done?