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Username007
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This is a problem I've been looking to solve for some time.
You must find a movement equation for an object in a gravitational field knowing traditional formulas of force and acceleration of gravity (see below).
absolute value of the acceleration at a distance 'r' from the centre of gravity of an object with mass 'm'
[itex]g=G\frac{m}{r^{2}}[/itex]
'r' as a movement equation
[itex]r=r(t)[/itex]
[itex]r''(t)=-g[/itex]
[itex]r''(t)=-G\frac{m}{r(t)^{2}}[/itex]
[itex]r''(t)r(t)^{2}=-Gm[/itex]
I don't really know what to do next. It seems that r(t) has at least one constant term and it's of degree>2 if it's a polynomial (as acceleration changes). I know nothing more than that.
Homework Statement
You must find a movement equation for an object in a gravitational field knowing traditional formulas of force and acceleration of gravity (see below).
Homework Equations
absolute value of the acceleration at a distance 'r' from the centre of gravity of an object with mass 'm'
[itex]g=G\frac{m}{r^{2}}[/itex]
'r' as a movement equation
[itex]r=r(t)[/itex]
[itex]r''(t)=-g[/itex]
The Attempt at a Solution
[itex]r''(t)=-G\frac{m}{r(t)^{2}}[/itex]
[itex]r''(t)r(t)^{2}=-Gm[/itex]
I don't really know what to do next. It seems that r(t) has at least one constant term and it's of degree>2 if it's a polynomial (as acceleration changes). I know nothing more than that.