Polar satellites:

Important Questions on Gravitation

EASY

Physics>Mechanics>Gravitation>Earth Satellites

A satellite is orbiting the Earth in a circular orbit of radius $R$ . Which one of the following statements is true?

MEDIUM

Physics>Mechanics>Gravitation>Earth Satellites

A satellite of mass $m$ is orbiting the earth (of radius $R$) at a height $h$ from its surface. The total energy of the satellite in terms of $g_o$ , the value of acceleration due to gravity at the earth's surface, is

EASY

Physics>Mechanics>Gravitation>Earth Satellites

If the axis of rotation of the earth were extended into space then it would pass close to -

HARD

Physics>Mechanics>Gravitation>Earth Satellites

A test particle is moving in a circular orbit in the gravitational field produced by a mass density $\rho \left(r\right)=\frac{K}{r^2}.$ Identify the current relation between the radius $\mathrm{R}$ of the particle’s orbit and its period $\mathrm{T}:$

EASY

Physics>Mechanics>Gravitation>Earth Satellites

A remote-sensing satellite of earth revolves in a circular orbit at a height of $0.25\times {10}^6$ m above the surface of earth. If earth's radius is $6.38\times {10}^6\mathrm{ }\mathrm{m}$ and $\mathrm{g}=9.8\mathrm{ }\mathrm{m }{\mathrm{s}}^{-2}$, then the orbital speed of the satellite is:

HARD

Physics>Mechanics>Gravitation>Earth Satellites

An asteroid is moving directly towards the centre of the earth. When at a distance of $10R$ ($R$ is the radius of the earth) from the centre of the earth, it has a speed of $12 \mathrm{km} {\mathrm{s}}^{-1}.$ Neglecting the effect of earth's atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is $11.2 \mathrm{k}\mathrm{m} {\mathrm{s}}^{-1})$ ? Give your answer to the nearest integer in $\mathrm{km} {\mathrm{s}}^{-1}$__________.

EASY

Physics>Mechanics>Gravitation>Earth Satellites

The ratio of the binding energy of a satellite at rest on earth's surface to the binding energy of a satellite of same mass revolving around the earth at a height $h$ above the earth's surface is $(R$= radius of the earth$)$.

EASY

Physics>Mechanics>Gravitation>Earth Satellites

A body is moving in a low circular orbit about a planet of mass $M$ and radius $R$. The radius of the orbit can be taken to be $R$ itself. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is: 

MEDIUM

Physics>Mechanics>Gravitation>Earth Satellites

What is the minimum energy required to launch a satellite of mass $\text{m}$ from the surface of a planet of mass $\text{M}$ and radius $\text{R}$ in a circular orbit at an altitude of $\text{2R}$?

MEDIUM

Physics>Mechanics>Gravitation>Earth Satellites

The minimum number of geostationary satellites required for uninterrupted global coverage is

MEDIUM

Physics>Mechanics>Gravitation>Earth Satellites

A spaceship orbits around a planet at a height of $20\mathrm{ }\mathrm{k}\mathrm{m}$ from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in $24$ hours around the planet?
[Given: Mass of planet $=8\times {10}^{22}\mathrm{ }\mathrm{k}\mathrm{g}$ ,
Radius of planet $=2\times {10}^6\mathrm{ }\mathrm{m},$
Gravitational constant $\mathrm{G}=6.67\times {10}^{-11}\mathrm{ }\mathrm{N}{\mathrm{m}}^2/\mathrm{k}{\mathrm{g}}^2$ ]

MEDIUM

Physics>Mechanics>Gravitation>Earth Satellites

Two satellites, $\mathrm{A}$ and $\mathrm{B}$, have masses $m$ and $2m$ respectively. $\mathrm{A}$ is in a circular orbit of radius $R$ and $\mathrm{B}$ is in a circular orbit of radius $2R$ around the earth. The ratio of their kinetic energies, $\frac{K_{\mathrm{A}}}{K_{\mathrm{B}}}$ is:

EASY

Physics>Mechanics>Gravitation>Earth Satellites

A satellite is orbiting close to the earth and has a kinetic energy $K$. The minimum extra kinetic energy required by it to just overcome the gravitation pull of the earth is

MEDIUM

Physics>Mechanics>Gravitation>Earth Satellites

A satellite is revolving in a circular orbit at a height $h$ from the earth's surface (radius of earth $R$; $\text{h}\text{<<}\text{R}$ ). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to (Neglect the effect of atmosphere.)

HARD

Physics>Mechanics>Gravitation>Earth Satellites

The mass density of a spherical galaxy varies as $\frac{\mathit{K}}{\mathit{r}}$ over a large distance $r$ from its center. In that region, a small star is in a circular orbit of radius $R$. Then the period of revolution,$T$ depends on $R$ as:

EASY

Physics>Mechanics>Gravitation>Earth Satellites

In an earth satellite moving in a circular orbit, a piece of metal (weighing $0.016 \mathrm{kg}$ on the earth) is weighed by a spring balance while the metal is suspended in water. If the density of metal is $8$ times of water density, then the recorded weight will be (g is acceleration due to gravity)

EASY

Physics>Mechanics>Gravitation>Earth Satellites

A planet is moving in a circular orbit. It completes $2$ revolutions in $360 \mathrm{days}$. What is its angular frequency?

EASY

Physics>Mechanics>Gravitation>Earth Satellites

The relative uncertainty in the period of a satellite orbiting around the earth is ${10}^{-2}$ . If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is:

MEDIUM

Physics>Mechanics>Gravitation>Earth Satellites

The energy required to take a satellite to a height $h$ above the Earth surface (radius of Earth $=6.4\times {10}^3 \mathrm{km}$ ) is $E_1$, and the kinetic energy required for the satellite to be in a circular orbit at this height is $E_2.$ The value of $h$ for which $E_1$ and $E_2$ are equal, is

HARD

Physics>Mechanics>Gravitation>Earth Satellites

Two stars of masses $3\times {10}^{31} \mathrm{kg}$ each, and at distance $2\times {10}^{11} \mathrm{m}$ rotate in a plane about their common centre of mass $\mathrm{O}.$ A meteorite passes through $\mathrm{O}$ moving perpendicular to the star's rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at $\mathrm{O}$ is ( Take Gravitational constant $G=6.67\times {10}^{-11} \mathrm{N} {\mathrm{m}}^2 {\mathrm{kg}}^{-2}$)