(D) The orbital velocity $v_0$ of a satellite revolving around a planet of mass $M$ at a distance $r$ from its center is given by the formula: $v_0 =

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The orbital velocity is inversely proportional to the square root of the radius of the orbit.

(D) The orbital velocity $v_0$ of a satellite revolving around a planet of mass $M$ at a distance $r$ from its center is given by the formula: $v_0 = \sqrt{\frac{GM}{r}}$.From this expression,it is clear that $v_0 \propto \frac{1}{\sqrt{r}}$.Therefore,the orbital velocity is inversely proportional to the square root of the radius of the orbit.Thus,option $D$ is the correct statement.

Class 11 Physics Gravitation Motion of Satellites in Circular Orbits and Planets in Elliptical Orbits

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Select the correct statement from the following:

A
The orbital velocity of a satellite increases with the radius of the orbit.
B
Escape velocity of a particle from the surface of the earth depends on the speed with which it is fired.
C
The time period of a satellite does not depend on the radius of the orbit.
D
The orbital velocity is inversely proportional to the square root of the radius of the orbit.

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Gravitation

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Motion of Satellites in Circular Orbits and Planets in Elliptical Orbits

An artificial satellite is moving around the Earth in a circular orbit with a speed equal to one-fourth the escape speed of a body from the surface of the Earth. The height of the satellite above the Earth's surface is ............ ($R$ is the radius of the Earth). (in $R$)

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In a satellite,if the time of revolution is $T$,then the kinetic energy $(K.E.)$ is proportional to:

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Two satellites $A$ and $B$ are revolving around the earth in orbits of heights $1.25 R_E$ and $19.25 R_E$ from the surface of the earth respectively,where $R_E$ is the radius of the earth. The ratio of the orbital speeds of the satellites $A$ and $B$ is (in $: 1$)

MediumAP EAMCET 2025

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The time period of a $1500 \,kg$ satellite is equal to the time period of rotation of the earth. The altitude of the satellite is nearly

DifficultAP EAMCET 2023

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Assertion $(A):$ An astronaut in an orbiting space station above the earth experiences weightlessness.
Reason $(R):$ An object moving around the earth under the influence of earth's gravitational force is in a state of 'free fall'.

MediumAIIMS 2015

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Select the correct statement from the following:

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An artificial satellite is moving around the Earth in a circular orbit with a speed equal to one-fourth the escape speed of a body from the surface of the Earth. The height of the satellite above the Earth's surface is ............ ($R$ is the radius of the Earth). (in $R$)

In a satellite,if the time of revolution is $T$,then the kinetic energy $(K.E.)$ is proportional to:

Two satellites $A$ and $B$ are revolving around the earth in orbits of heights $1.25 R_E$ and $19.25 R_E$ from the surface of the earth respectively,where $R_E$ is the radius of the earth. The ratio of the orbital speeds of the satellites $A$ and $B$ is (in $: 1$)

The time period of a $1500 \,kg$ satellite is equal to the time period of rotation of the earth. The altitude of the satellite is nearly

Assertion $(A):$ An astronaut in an orbiting space station above the earth experiences weightlessness.Reason $(R):$ An object moving around the earth under the influence of earth's gravitational force is in a state of 'free fall'.

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Assertion $(A):$ An astronaut in an orbiting space station above the earth experiences weightlessness.
Reason $(R):$ An object moving around the earth under the influence of earth's gravitational force is in a state of 'free fall'.