- #1

DavidTheGreat

<Moderator's note: Moved from elsewhere and therefore no template.>

I'm trying to calculate the distance of free fall for an object with zero tangential velocity but a given radial velocity at a given height over a given period of time. This calculation cannot assume that g is constant as it deals with orbital heights. These calculations are needed for an orbital ring that I'm designing. Here is my working out so far.

1.) F=ma

2.) F=GMm/R^2

Sub 1.) into 2.)

ma=GMm/R^2

a=GM/R^2

v=da/dt

v=d/dt(GM/R^2)

v=GM d/dt(1/R^2)

R=dv/dt

R=GM d^2/dt^2(1/R^2)

I can't figure out how to solve this second order differential equation. Is there a better way of doing it/where did I go wrong?

I'm trying to calculate the distance of free fall for an object with zero tangential velocity but a given radial velocity at a given height over a given period of time. This calculation cannot assume that g is constant as it deals with orbital heights. These calculations are needed for an orbital ring that I'm designing. Here is my working out so far.

1.) F=ma

2.) F=GMm/R^2

Sub 1.) into 2.)

ma=GMm/R^2

a=GM/R^2

v=da/dt

v=d/dt(GM/R^2)

v=GM d/dt(1/R^2)

R=dv/dt

R=GM d^2/dt^2(1/R^2)

I can't figure out how to solve this second order differential equation. Is there a better way of doing it/where did I go wrong?

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