A star like the sun has several bodies moving around it at different distances. Consider that all of them are moving in circular orbits. Let r be the distance of the body from the centre of the star and let its linear velocity be v, angular velocity ω, kinetic energy K, gravitational potential energy U, total energy E and angular momentum l. As the radius r of the orbit increases, determine which of the above quantities increase and which ones decrease.
Given:
Radius of the orbit of planets = r
Let the mass of the sun be M and the planet be m.
(a) The force on an object revolving around the star is given by
Therefore, linear velocity v is inversely proportional to square root of r and hence when r increases, v decreases.
(b) The angular velocity ω is given by
Therefore, when r increases, ω decreases.
(c) The kinetic energy K is given by,
Therefore, as r increases, K decreases.
(d) The potential energy U is given by,
Therefore, as r increases U becomes less negative or increases.
(e) The total energy E is given by,
Therefore, as r increases E becomes less negative or increases.
(f) The angular momentum L is given by,
Therefore, as r increases, L increases.
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