A planet moves around the Sun in an elliptical orbit as shown. Eccentricity of ellipse is 1 2 . Time taken by planet to move from D to B ( D → A → B ) and B to D ( B → C → D ) are respectively T D A B and T B C D

velocity of planet of point B is 3 2 v 2

T D A B T B C D = π + 2 π - 2

velocity of planet of point B is 2 v 2

A planet moves around the Sun in an elliptical orbit as shown. Eccentricity of ellipse is 1 2 . Time taken by planet to move from D to B ( D → A → B ) and B to D ( B → C → D ) are respectively T D A B and T B C D

velocity of planet of point B is 3 2 v 2

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A planet moves around the Sun in an elliptical orbit as shown. Eccentricity of ellipse is $\frac{1}{2}$ . Time taken by planet to move from $D$ to $B (D \to A \to B)$ and $B$ to $D$ $(B \to C \to D)$ are respectively $T_{D A B}$ and $T_{B C D}$

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Important Questions on Gravitation

HARD

Physics>Mechanics>Gravitation>Motion of Planets and Satellites in Circular Orbits

Two satellites

A

and

B

of masses

200 kg

and

400 kg

are revolving round the earth at height of

600 km

and

1600 km

respectively. If

T_{A}

and

T_{B}

are the time periods of

A

and

B

respectively then the value of

T_{B} - T_{A}

Question Image

[ Given : radius of earth $= 6400 km,$ mass of earth $= 6 \times 10^{24} kg$ ]

EASY

Physics>Mechanics>Gravitation>Motion of Planets and Satellites in Circular Orbits

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>Motion of Planets and Satellites in Circular Orbits

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}}

EASY

Physics>Mechanics>Gravitation>Motion of Planets and Satellites in Circular Orbits

The time period of an earth satellite in circular orbit is independent of

MEDIUM

Physics>Mechanics>Gravitation>Motion of Planets and Satellites in Circular Orbits

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.)

EASY

Physics>Mechanics>Gravitation>Motion of Planets and Satellites in Circular Orbits

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 .

EASY

Physics>Mechanics>Gravitation>Motion of Planets and Satellites in Circular Orbits

A planet is moving in a circular orbit. It completes

2

revolutions in

360 days

. What is its angular frequency?

EASY

Physics>Mechanics>Gravitation>Motion of Planets and Satellites in Circular Orbits

Two satellites of masses

m

and

3 m

revolve around the earth in circular orbits of radii

r & 3 r

respectively. The ratio of orbital speeds of the satellites respectively is

HARD

Physics>Mechanics>Gravitation>Motion of Planets and Satellites in Circular Orbits

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 :

MEDIUM

Physics>Mechanics>Gravitation>Motion of Planets and Satellites in Circular Orbits

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}

]

MEDIUM

Physics>Mechanics>Gravitation>Motion of Planets and Satellites in Circular Orbits

The planet Mars has two moons, if one of them has a period

7

hours,

30

minutes and an orbital radius of

9.0 \times 10^{3} km .

Find the mass of Mars.

\{

Given

\frac{4 π^{2}}{G} = 6 \times 10^{11} N^{- 1} m^{- 2} {kg}^{2}\}

EASY

Physics>Mechanics>Gravitation>Motion of Planets and Satellites in Circular Orbits

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>Motion of Planets and Satellites in Circular Orbits

A geostationary satellite is taken to a new orbit such that its distance from centre of the earth is doubled. Then find the time period of this satellite in the new orbit.

EASY

Physics>Mechanics>Gravitation>Motion of Planets and Satellites in Circular Orbits

Consider two satellites

S_{1}

and

S_{2}

with periods of revolution

1 hr

and

8 hr

respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite

S_{1}

to the angular velocity of satellite

S_{2}

is:

EASY

Physics>Mechanics>Gravitation>Motion of Planets and Satellites in Circular Orbits

Two satellites

A

and

B

are orbiting a planet in circular orbits with radii

2 R

and

R

respectively. If the speed of satellite

A

2 v

, then the speed of satellite

B

EASY

Physics>Mechanics>Gravitation>Motion of Planets and Satellites in Circular Orbits

A satellite is orbiting just above the surface of the earth with period

T

. If

d

is the density of the earth and

G

is the universal constant of gravitation, the quantity

\frac{3 π}{G d}

represents :

EASY

Physics>Mechanics>Gravitation>Motion of Planets and Satellites in Circular Orbits

The time period of a satellite, revolving above earth's surface at a height equal to

R

will be (Given

g = π^{2} m s^{- 2}, R =

radius of earth)

HARD

Physics>Mechanics>Gravitation>Motion of Planets and Satellites in Circular Orbits

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>Motion of Planets and Satellites in Circular Orbits

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

EASY

Physics>Mechanics>Gravitation>Motion of Planets and Satellites in Circular Orbits

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:

A planet moves around the Sun in an elliptical orbit as shown. Eccentricity of ellipse is 12. Time taken by planet to move from D to B(D→A→B) and B to D (B→C→D) are respectively TDAB and TBCD

Important Questions on Gravitation

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A planet moves around the Sun in an elliptical orbit as shown. Eccentricity of ellipse is $\frac{1}{2}$ . Time taken by planet to move from $D$ to $B (D \to A \to B)$ and $B$ to $D$ $(B \to C \to D)$ are respectively $T_{D A B}$ and $T_{B C D}$