mlazos
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we know from the equation of motion that
\frac{d^2r}{dt^2}=a
where a is the acceleration
for the gravity field we have
a=\frac{GM}{r^2}
So we get
\frac{d^2r}{dt^2}=\frac{GM}{r^2}
\frac{(R1^3-R2^3)}{3}\frac{dr}{dt}=GMt
\frac{dr}{dt}=\frac{3GMt}{R1^3-R2^3}
u=\sqrt{\frac{3GMt}{R1^3-R2^3}}
If we integrate one time from R1 to R2 shouldn't we get the speed?
Because from the equation og energy we get a different result
u=\sqrt{2GM}\sqrt{\frac{R1-R2}{R1*R2}}
So where am i wrong?
\frac{d^2r}{dt^2}=a
where a is the acceleration
for the gravity field we have
a=\frac{GM}{r^2}
So we get
\frac{d^2r}{dt^2}=\frac{GM}{r^2}
\frac{(R1^3-R2^3)}{3}\frac{dr}{dt}=GMt
\frac{dr}{dt}=\frac{3GMt}{R1^3-R2^3}
u=\sqrt{\frac{3GMt}{R1^3-R2^3}}
If we integrate one time from R1 to R2 shouldn't we get the speed?
Because from the equation og energy we get a different result
u=\sqrt{2GM}\sqrt{\frac{R1-R2}{R1*R2}}
So where am i wrong?
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