$A$ 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 $\omega$,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.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) For a body of mass $m$ revolving around a star of mass $M$ in a circular orbit of radius $r$:
$1$. Linear velocity: $v = \sqrt{\frac{GM}{r}}$. As $r$ increases,$v$ decreases.
$2$. Angular velocity: $\omega = \frac{v}{r} = \sqrt{\frac{GM}{r^3}}$. As $r$ increases,$\omega$ decreases.
$3$. Kinetic energy: $K = \frac{1}{2}mv^2 = \frac{GMm}{2r}$. As $r$ increases,$K$ decreases.
$4$. Gravitational potential energy: $U = -\frac{GMm}{r}$. As $r$ increases,$U$ increases (becomes less negative).
$5$. Total energy: $E = K + U = -\frac{GMm}{2r}$. As $r$ increases,$E$ increases (becomes less negative).
$6$. Angular momentum: $l = mvr = m\sqrt{GMr}$. As $r$ increases,$l$ increases.

Explore More

Similar Questions

The minimum energy required to launch a satellite of mass $m$ from the surface of the Earth of mass $M$ and radius $R$ into a circular orbit at an altitude of $2R$ from the surface of the Earth is:

$A$ satellite of $10^3 \text{ kg}$ mass is revolving in a circular orbit of radius $2R$. If $\frac{10^4 R}{6} \text{ J}$ of energy is supplied to the satellite,it would revolve in a new circular orbit of radius: (use $g = 10 \text{ m/s}^2$,$R = \text{radius of earth}$) (in $R$)

$A$ launching vehicle carrying an artificial satellite of mass $m$ is set for launch on the surface of the earth of mass $M$ and radius $R$. If the satellite is intended to move in a circular orbit of radius $7R$,the minimum energy required to be spent by the launching vehicle on the satellite is ($G$ is the gravitational constant).

$A$ satellite of mass $m$ is orbiting the Earth (of radius $R$) at a height equal to the radius of the Earth. The total energy of the satellite in terms of $g$ (acceleration due to gravity on Earth's surface) is

$A$ satellite of earth of mass $m$ is moved from an orbital radius of $2R$ to $3R$. Calculate the minimum work done.

Difficult
View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo