(B) The orbital speed $v$ of a satellite revolving around a planet of mass $M$ at a distance $r$ from its center is given by the formula $v = \sqrt{\f

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(B) The orbital speed $v$ of a satellite revolving around a planet of mass $M$ at a distance $r$ from its center is given by the formula $v = \sqrt{\frac{GM}{r}}$.From this expression,it is clear that the orbital speed $v$ is independent of the mass of the satellite ($m_1$ or $m_2$).However,the orbital speed $v$ is inversely proportional to the square root of the orbital radius $r$ $(v \propto \frac{1}{\sqrt{r}})$.Given that $r_1 > r_2$,it follows that $\frac{1}{\sqrt{r_1}} Therefore,$v_1 < v_2$.

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

Easy

Two satellites of masses $m_1$ and $m_2$ $(m_1 > m_2)$ are revolving around the Earth in circular orbits of radii $r_1$ and $r_2$ $(r_1 > r_2)$ respectively. Which of the following statements is true regarding their speeds $v_1$ and $v_2$?

A
$v_1 = v_2$
B
$v_1 < v_2$
C
$v_1 > v_2$
D
$\frac{v_1}{r_1} = \frac{v_2}{r_2}$

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Class 11

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Gravitation

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Motion of Satellites in Circular Orbits and Planets in Elliptical Orbits

The time period of a geostationary satellite is

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The earth (mass $M = 6 \times 10^{24} \ kg$) revolves around the sun with an angular velocity $\omega = 2 \times 10^{-7} \ rad/s$ in a circular orbit of radius $R = 1.5 \times 10^8 \ km$. The force exerted by the sun on the earth in newtons is:

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The maximum and minimum distances of a comet from the sun are $8 \times 10^{12} \, m$ and $1.6 \times 10^{12} \, m$. If its velocity when nearest to the sun is $60 \, m/s$,what will be its velocity in $m/s$ when it is farthest?

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Give the uses of geostationary satellite and polar satellite.

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The time period of revolution of a satellite orbiting very close to a planet of radius $R$ is $T$. What is the period of revolution around another planet,whose radius is $3R$ but having the same density?

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Two satellites of masses $m_1$ and $m_2$ $(m_1 > m_2)$ are revolving around the Earth in circular orbits of radii $r_1$ and $r_2$ $(r_1 > r_2)$ respectively. Which of the following statements is true regarding their speeds $v_1$ and $v_2$?

Similar Questions

The time period of a geostationary satellite is

The earth (mass $M = 6 \times 10^{24} \ kg$) revolves around the sun with an angular velocity $\omega = 2 \times 10^{-7} \ rad/s$ in a circular orbit of radius $R = 1.5 \times 10^8 \ km$. The force exerted by the sun on the earth in newtons is:

The maximum and minimum distances of a comet from the sun are $8 \times 10^{12} \, m$ and $1.6 \times 10^{12} \, m$. If its velocity when nearest to the sun is $60 \, m/s$,what will be its velocity in $m/s$ when it is farthest?

Give the uses of geostationary satellite and polar satellite.

The time period of revolution of a satellite orbiting very close to a planet of radius $R$ is $T$. What is the period of revolution around another planet,whose radius is $3R$ but having the same density?

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