Quenstion about netwonian mechanics.(adsbygoogle = window.adsbygoogle || []).push({});

We have a small body that is moving against a very massive object with big density.

For a given time t i want to know what can be the maximum distance of this object.

So we have the mass of the big object M , the mass of the small m with speed Ua and the time t.

the velocity at any moment is Ua+Uf where Uf is the speed because of the acceleration of the gravity.

F=M*m*G/r^2

d(dr/dt)/dt=a

where a is the acceleration

a=M*G/r^2

r=R+s where R is the radius of the object and s the distance tha the object traveled at time t. I need an equation to find the s.

Dont forget that the object begins with a speed Ua not from 0 speed.

thanks and please quick

Of course the gravity force is not constant but change with distance,

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# Gravity-free Fall

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