What is the effect of acceleration due to gravity on the escape velocity from am object of mass m? I don't even know where to start with this. If the object has radius r and mass m and the acceleration due to gravity on the object is a, how do I find the escape velocity of another object from the first one?
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5$\begingroup$ Possible duplicate of Escape velocity from Earth and many others. $\endgroup$– garypCommented Oct 16, 2016 at 18:45
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$\begingroup$ @garyp I still don't understand after looking through the link, the question in the link is whether the angle of projection of an object from the earth's centre affects it's escape velocity value from the earth. Mine is to find how the acceleration due to gravity on an object O affects the escape velocity from it. $\endgroup$– lekaraneCommented Oct 16, 2016 at 18:54
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When standing on the surface of the earth, you have a potential energy of $U = -G \frac{Mm}{R}$.
In order to escape this gravitational well you need to gain the same amount of kinetic energy $E = \frac{1}{2}mv^2$.
By Equating the two and solving for velocity $v = \sqrt{\frac{GM}{R}}$ we can find the velocity required to fulfil this requirement.
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$\begingroup$ What I need is how to find the escape velocity from the object, not the earth. Is G always constant regardless of the size of the body or value of acceleration due to gravity? Take for example the gravitational constant on the moon. $\endgroup$– lekaraneCommented Oct 16, 2016 at 21:10
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1$\begingroup$ $G$ is known as universal gravitational constant which is fixed. Don't mess up with the acceleration due to gravity $g=\dfrac{GM}{R^{2}}$ which is depending on what stellar object you're referring. $\endgroup$ Commented Oct 16, 2016 at 21:27
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$\begingroup$ If you're on the moon, use the mass, M, and radius, R, of the moon. If you're on planet X, use the mass, M, and radius, R, of planet X. $\endgroup$– Bill NCommented Oct 17, 2016 at 17:09