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Geo-stationary satellite revolves in (equatorial/ polar) orbit of earth.

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Important Questions on Gravitation

MEDIUM

Physics>Mechanics>Gravitation>Geostationary and Polar Satellites

Define binding energy and obtain an expression for binding energy of a satellite revolving in a circular orbit round the earth.

EASY

Physics>Mechanics>Gravitation>Geostationary and Polar Satellites

A satellite is launched to a distance

r

from the centre of the earth to have a circular orbit around the earth. Its orbital velocity to maintain this orbit is (mass of the earth as

M_{E}

)

EASY

Physics>Mechanics>Gravitation>Geostationary and Polar Satellites

A person jumps from the

5^{th}

storey of a building with load on his head. The weight experienced by him before reaching the earth will be

EASY

Physics>Mechanics>Gravitation>Geostationary and Polar Satellites

A geostationary satellite is orbiting around an arbitrary planet

P

at a height of

11 R

above the surface of

P

R

being the radius of

P

. The time period of another satellite in hours at a height of

2 R

from the surface of

P

is ________ has the time period of

24 hours .

MEDIUM

Physics>Mechanics>Gravitation>Geostationary and Polar Satellites

A spaceship orbits around a planet at a height of

20 k 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} k g

,
Radius of planet

= 2 \times 10^{6} m,

Gravitational constant

G = 6.67 \times 10^{- 11} N m^{2} / k g^{2}

]

EASY

Physics>Mechanics>Gravitation>Geostationary and Polar Satellites

A geostationary satellite is orbiting the earth at a height

6 R

above the surface of the earth, where

R

is the radius of the earth. The time period of another satellite at a height

(2.5 R)

from the surface of the earth is

MEDIUM

Physics>Mechanics>Gravitation>Geostationary and Polar Satellites

Two satellites

A

and

B

are revolving with critical velocities

v_{A}

and

v_{B}

around the earth, in circular orbits of radii

R

and

2 R

respectively. The ratio

\frac{v_{A}}{v_{B}}

MEDIUM

Physics>Mechanics>Gravitation>Geostationary and Polar Satellites

Two satellites,

A

and

B

, have masses

m

and

2 m

respectively.

A

is in a circular orbit of radius

R

and

B

is in a circular orbit of radius

2 R

around the earth. The ratio of their kinetic energies,

\frac{K_{A}}{K_{B}}

is:

HARD

Physics>Mechanics>Gravitation>Geostationary and Polar Satellites

The mass density of a spherical galaxy varies as

\frac{K}{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>Geostationary and Polar 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>Geostationary and Polar Satellites

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

MEDIUM

Physics>Mechanics>Gravitation>Geostationary and Polar Satellites

A satellite is revolving in a circular orbit at a height

h

from the earth's surface (radius of earth

R

;

h << 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.)

MEDIUM

Physics>Mechanics>Gravitation>Geostationary and Polar Satellites

The ratio of escape velocity at earth

(v_{e})

to the escape velocity at a planet

(v_{p})

whose radius and mean density are twice as that of earth is:

EASY

Physics>Mechanics>Gravitation>Geostationary and Polar Satellites

A geostationary satellite orbits around the earth in a circular orbit of radius

36000 km

. Then, the time period of a sky satellite orbiting a few

100 km

above the earth's surface

(R = 64000 km)

will approximately be

HARD

Physics>Mechanics>Gravitation>Geostationary and Polar Satellites

Two stars of masses

3 \times 10^{31} kg

each, and at distance

2 \times 10^{11} m

rotate in a plane about their common centre of mass

O .

A meteorite passes through

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

O

is ( Take Gravitational constant

G = 6.67 \times 10^{- 11} N m^{2} {kg}^{- 2}

)

MEDIUM

Physics>Mechanics>Gravitation>Geostationary and Polar Satellites

The energy required to take a satellite to a height

h

above the Earth surface (radius of Earth

= 6.4 \times 10^{3} 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

MEDIUM

Physics>Mechanics>Gravitation>Geostationary and Polar Satellites

A satellite is moving with a constant speed

v

in circular orbit around the earth. An object of mass 'm' is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is:

EASY

Physics>Mechanics>Gravitation>Geostationary and Polar Satellites

A planet is moving in a circular orbit. It completes

2

revolutions in

360 days

. What is its angular frequency?

HARD

Physics>Mechanics>Gravitation>Geostationary and Polar Satellites

A test particle is moving in a circular orbit in the gravitational field produced by a mass density

ρ (r) = \frac{K}{r^{2}} .

Identify the current relation between the radius

R

of the particle’s orbit and its period

T :

EASY

Physics>Mechanics>Gravitation>Geostationary and Polar 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:

Geo-stationary satellite revolves in (equatorial/ polar) orbit of earth.

Important Questions on Gravitation

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