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A satellite $S$ is moving in an elliptical orbit around earth. The mass of the satellite is very small compared to the mass of the earth.

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Important Questions on Gravitation

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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

)

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 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

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

;

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>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} 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

EASY

Physics>Mechanics>Gravitation>Earth Satellites

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

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:

HARD

Physics>Mechanics>Gravitation>Earth 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:

MEDIUM

Physics>Mechanics>Gravitation>Earth 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:

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} m

and

g = 9.8 m s^{- 2}

, then the orbital speed of the satellite is:

HARD

Physics>Mechanics>Gravitation>Earth 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 :

HARD

Physics>Mechanics>Gravitation>Earth Satellites

A body is thrown from the surface of the earth with velocity

u m s^{- 1}

. The maximum height in meter above the surface of the earth up to which it will reach is (

R =

radius of the earth,

g =

acceleration due to gravity)

MEDIUM

Physics>Mechanics>Gravitation>Earth 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>Earth Satellites

A satellite is orbiting the Earth in a circular orbit of radius

R

. Which one of the following statements is true?

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

EASY

Physics>Mechanics>Gravitation>Earth Satellites

A planet is moving in a circular orbit. It completes

2

revolutions in

360 days

. What is its angular frequency?

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

m

from the surface of a planet of mass

M

and radius

R

in a circular orbit at an altitude of

2R

HARD

Physics>Mechanics>Gravitation>Earth 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>Earth Satellites

The kinetic energies of a planet in an elliptical orbit about the Sun, at positions,

A, B

and

C

are

K_{A}, K_{B} a n d K_{C}

, respectively.

A C

is the major axis and

S B

is perpendicular to

A C

at the position of the Sun

S

as shows in the figure. Then

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A satellite S is moving in an elliptical orbit around earth. The mass of the satellite is very small compared to the mass of the earth.

Important Questions on Gravitation

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A satellite $S$ is moving in an elliptical orbit around earth. The mass of the satellite is very small compared to the mass of the earth.