- #1
Vicara
- 38
- 4
Well, first of all i want to apologize about my english skills hahaha
I have been trying to calculate a time formula for free falling object through large distances (or weak gravitational fields) and my results don´t have much sense (I test my results in a quite realistic game called Algodoo)
What I have calculated is
g(r) = G⋅(M/r2) and as g = dv/dt = dv/dr ⋅ dr/dv = dv/dr ⋅ v
we got
∫v⋅dv = ∫G⋅M/r2 = 0.5⋅v2 = G⋅M⋅(-1/r)
v(r) = √(2⋅G⋅M⋅(-1/r)) = dr/dt now we integrate both sides ∫dt = ∫1/[ √(2⋅G⋅M⋅(-1/r) ] ⋅dr
and finally
t = t0 + (2/3)⋅√(r3/-2⋅G⋅M)
Please tell me what is wrong or if what i´m doing makes sense
Thanks!
I have been trying to calculate a time formula for free falling object through large distances (or weak gravitational fields) and my results don´t have much sense (I test my results in a quite realistic game called Algodoo)
What I have calculated is
g(r) = G⋅(M/r2) and as g = dv/dt = dv/dr ⋅ dr/dv = dv/dr ⋅ v
we got
∫v⋅dv = ∫G⋅M/r2 = 0.5⋅v2 = G⋅M⋅(-1/r)
v(r) = √(2⋅G⋅M⋅(-1/r)) = dr/dt now we integrate both sides ∫dt = ∫1/[ √(2⋅G⋅M⋅(-1/r) ] ⋅dr
and finally
t = t0 + (2/3)⋅√(r3/-2⋅G⋅M)
Please tell me what is wrong or if what i´m doing makes sense
Thanks!