Yes, ##M## remains stationary relative to ##m##.
I would be happy to derive an equation for ##M## ~ ##m## so ##M## isn't stationary, but I don't have enough knolige in calculus.
This way is much clearer.
I think Ill learn more calculus and then try to get to get to this equation. Or try another simular one( I want to calculate V and t for a free falling object with air resistance
)
a = G * M
v(x) = √(2 *a)/x
1/v(x) = 1/√(2 *a)/x = √x / √2a
∫ 1/v(x) dx =
=∫ √x / √2a dx =
=1/√2a ∫ √x =
=1/√2a * x1.5/1.5 =
= √2 * x1.5/3a
I'm not sure it's correct.
And I reread post #27 about this equation but I don't undersatnd how to apply it.
From what I understand this is t, and It...
I got 2000 seconds, which is the only answer that is in the limit 1414 < t < 2828 seconds.
I found that the average accelerationis 5 m/s. a0 = 2.5 m/s2 and af = 10 m/s2.
I rejected this idea twice already but becuse it's the on;y one that gives an answer in the limit I tried it again.
The...
I'm a 10th grade student and I'm very interested in railway engineering. Especially railway vehicle engineering.
What are the requirements for that kind of profession?
Using conversation of energy I found V(r) => Vfinal.
And I know the function a(r) = G × M / r2.
So when V0 = 0 ,∫ a(r) dr = (Vfinal * Δt)*(Δt/Vavg) = Vfinal * Vavg.
Δt = Δx/Vavg.
I found a way to get the time.But because I have to learn more calculus I can't derive an X(t) function.
I'm learning calculus alone amd when I will understand how to solve a deferential equation Ill try to derive an X(t) function.
So I think rcgldr can release his analysis now.
Yeah, its impossible to get v(t). I'm now just searching for x(t).
I know there are a lot of solutions here but I don't really understand them. I think I have to get to them myself to fully understand this.