we know from the equation of motion that(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{d^2r}{dt^2}=a[/tex]

where a is the acceleration

for the gravity field we have

[tex]a=\frac{GM}{r^2}[/tex]

So we get

[tex]\frac{d^2r}{dt^2}=\frac{GM}{r^2}[/tex]

[tex]\frac{(R1^3-R2^3)}{3}\frac{dr}{dt}=GMt[/tex]

[tex]\frac{dr}{dt}=\frac{3GMt}{R1^3-R2^3}[/tex]

[tex]u=\sqrt{\frac{3GMt}{R1^3-R2^3}}[/tex]

If we integrate one time from R1 to R2 shouldnt we get the speed?

Because from the equation og energy we get a different result

[tex]u=\sqrt{2GM}\sqrt{\frac{R1-R2}{R1*R2}}[/tex]

So where am i wrong?

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# Homework Help: Speed and Gravity

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