Orbital Motion of a Satellite

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JEE Main 2021, 1 Sep. Shift-II

LEVELJEE Advanced

Two satellites revolve around a planet in coplanar circular orbits in anti-clockwise direction. Their period of revolutions are $1 h$ and $8 h$ , respectively. The radius of the orbit of nearer satellite is $2 \times 1 0^{3} km$ . The angular speed of the farther satellite as observed from the nearer satellite at the instant when both the satellites are closest is $\frac{π}{x} rad h^{- 1}$ , where $x$ is ……… .

JEE Main 2020

LEVELJEE Main

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

(A)

(B)

\frac{1}{2}

(C)

2

(D)

JEE Main 2021, 24 Feb Shift-I

LEVELJEE Main

Consider two satellites $S_{1}$ and $S_{2}$ with periods of revolution 1 h and 8 h 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

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

(A)

the mass of the satellite

(B)

radius of its orbit

(C)

both the mass and radius of the orbit

(D)

neither the mass of the satellite nor the radius of its orbit

JEE Main 2019 (09 Jan Shift-II)

LEVELJEE Main

The energy required to take a satellite to a height ' $h$ ' above earth surface (where, radius of earth $= 6.4 \times 1 0^{3}$ km) is $E_{1}$ and 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

(A)

3.2 \times 1 0^{3}

(B)

1.28 \times 1 0^{4}

(C)

6.4 \times 1 0^{3}

(D)

1.6 \times 1 0^{3}

JEE Main 2020, 6 Sep Shift-I

LEVELJEE Main

A satellite is in an elliptical orbit around a planet $P$ . It is observed that the velocity of the satellite when it is farthest from the planet is 6 times less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is

(A)

1 : 6

(B)

1 : 3

(C)

1 : 2

(D)

3 : 4

JEE Main 2020, 7 Jan Shift-I

LEVELJEE Advanced

A satellite of mass $m$ is launched vertically upwards with an initial speed $u$ from the surface of the earth. After it reaches height $R$ ( $R =$ radius of the earth), it ejects a rocket of mass $\frac{m}{10}$ , so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is ( $G$ is the gravitational constant, $M$ is the mass of the earth)

(A)

\frac{3 m}{8} (u + \frac{5 GM}{6 R})^{2}

(B)

\frac{m}{20} (u - \frac{2 GM}{3 R})^{2}

(C)

\frac{m}{20} (u^{2} + \frac{113}{200} \frac{GM}{R})

(D)

5 m (u^{2} - \frac{119}{200} \frac{GM}{R})

JEE Main 2019, 12 Jan Shift-II

LEVELJEE Main

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, $T_{A} / T_{B}$ is

(A)

\frac{1}{2}

(B)

2

(C)

\frac{1}{2}

(D)

1

JEE Main 2019, 12 Jan Shift-I

LEVELJEE Advanced

A satellite of mass $M$ is in a circular orbit of radius $R$ about the centre of the earth. A meteorite of the same mass falling towards the earth collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same just before the collision. The subsequent motion of the combined body will be

(A)

in the same circular orbit of radius

R

(B)

in an elliptical orbit

(C)

such that it escapes to infinity

(D)

in a circular orbit of a different radius

JEE Main 2021, 27 July Shift-II

LEVELJEE Main

The planet Mars has two Moons, if one of them has a period 7 h, 30 min and an orbital radius of $9.0 \times 1 0^{3}$ km. Find the mass of Mars. $[Take, \frac{4 π ^{2}}{G} = 6 \times 1 0^{11} N^{- 1} m^{- 2} kg^{2}]$

(A)

5.96 \times 1 0^{19}

(B)

3.25 \times 1 0^{21}

(C)

7.02 \times 1 0^{25}

(D)

6.00 \times 1 0^{23}

LEVELJEE Main

If suddenly the gravitational force of attraction between earth and a satellite revolving around it becomes zero, then the satellite will

(A)

continue to move in its orbit with same velocity

(B)

move tangentially to the original orbit with the same velocity

(C)

become stationary in its orbit

(D)

move towards the earth

JEE Main 2020, 2 Sep Shift-I

LEVELJEE Advanced

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

(A)

T \propto R

(B)

T^{2} \propto R^{3}

(C)

T^{2} \propto R

(D)

T^{2} \propto \frac{1}{R ^{3}}

JEE Main 2019, 11 Jan Shift-I

LEVELJEE Main

A satellite is revolving in a circular orbit at a height $h$ from the earth surface such that $h << R$ , where $R$ is the radius of the earth. Assuming that the effect of earth's atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is

(A)

\frac{g R}{2}

(B)

g R

(C)

2 g R

(D)

g R (2 - 1)

JEE Main 2019, 10 April Shift-II

LEVELJEE Advanced

A spaceship orbits around a planet at a height of $20 km$ 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? [Take, mass of planet = $8 \times 1 0^{22} kg$ , radius of planet = $2 \times 1 0^{6} m$ , gravitational constant $G = 6.67 \times 1 0^{- 11} N-m^{2} / kg^{2}$ ]

A satellite of mass $m$ revolves around the earth of radius $R$ at a height $x$ from its surface. If $g$ is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

(A)

g x

(B)

\frac{g R}{R - x}

(C)

\frac{g R ^{2}}{R + x}

(D)

(\frac{g R ^{2}}{R + x})^{1/2}

JEE Main 2019, 9 April Shift-II

LEVELJEE Advanced

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

(A)

\frac{T ^{2}}{R ^{3}}

is a constant

(B)

\frac{T}{R ^{2}}

is a constant

(C)

T R

is a constant

(D)

\frac{T}{R}

is a constant

JEE Main 2021, 25 Feb Shift-I

LEVELJEE Advanced

Two satellites $A$ and $B$ of masses $200 kg$ and $400 kg$ are revolving around 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 $T_{B} - T_{A}$ is (Given, radius of Earth $= 6400 km$ , mass of Earth $= 6 \times 1 0^{24} kg$ )

(A)

1.33 \times 1 0^{3} s

(B)

3.33 \times 1 0^{2} s

(C)

4.24 \times 1 0^{3} s

(D)

4.24 \times 1 0^{2} s

JEE Main 2013

LEVELJEE Main

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 $2 R$ ?

(A)

\frac{5 G m M}{6 R}

(B)

\frac{2 G m M}{3 R}

(C)

\frac{G m M}{2 R}

(D)

\frac{G m M}{3 R}

JEE Main 2020, 3 Sep Shift-I

LEVELJEE Advanced

A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth's radius $R_{e}$ . By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion, so that it becomes $\frac{3}{2}$ times larger. Due to this, the farthest distance from the centre of the earth that the satellite reaches is $R$ . Value of $R$ is

(A)

4 R_{e}

(B)

2.5 R_{e}

(C)

3 R_{e}

(D)

2 R_{e}

JEE Main 1987

LEVELJEE Main

A geostationary satellite is orbiting the earth at a height of $6 R$ above the surface of the earth where $R$ is the radius of earth. The time period of another satellite at a height of $2.5 R$ from the surface of the earth is _________ hours.

JEE Advanced 2008

LEVELJEE Main

Assertion: An astronaut in an orbiting space station above the earth experiences weightlessness. Reason: An object moving around the earth under the influence of earth's gravitational force is in a state of 'free-fall'.

(A)

If Assertion is true, Reason is true; Reason is the correct explanation for Assertion

(B)

If Assertion is true, Reason is true; Reason is not a correct explanation for Assertion

(C)

If Assertion is true; Reason is false

(D)

If Assertion is false; Reason is true

JEE Advanced (2006)

LEVELJEE Main

A double star system consists of two stars $A$ and $B$ which have time periods $T_{A}$ and $T_{B}$ . Radius $R_{A}$ and $R_{B}$ and mass $M_{A}$ and $M_{B}$ . Choose the correct option.

(A)

T_{A} > T_{B}

then

R_{A} > R_{B}

(B)

T_{A} > T_{B}

then

M_{A} > M_{B}

(C)

(\frac{T _{A}}{T _{B}})^{2} = (\frac{R _{A}}{R _{B}})^{3}

(D)

T_{A} = T_{B}

JEE Advanced 1990

LEVELJEE Main

An artificial satellite is moving in a circular orbit around the Earth with a speed equal to half the magnitude of escape velocity from the Earth. (1990) (a) Determine the height of the satellite above the earth's surface. (b) If the satellite is stopped suddenly in its orbit and allowed to fall freely onto the Earth, find the speed with which it hits the surface of the Earth.

JEE Advanced 2018

LEVELJEE Advanced

A planet of mass $M$ , has two natural satellites with masses $m_{1}$ and $m_{2}$ . The radii of their circular orbits are $R_{1}$ and $R_{2}$ , respectively. Ignore the gravitational force between the satellites. Define $v_{1}, L_{1}, K_{1}$ and $T_{1}$ to be respectively, the orbital speed, angular momentum, kinetic energy and time period of revolution of satellite 1; and $v_{2}, L_{2}, K_{2}$ and $T_{2}$ to be the corresponding quantities of satellite 2. Given, $\frac{m _{1}}{m _{2}} = 2$ and $\frac{R _{1}}{R _{2}} = \frac{1}{4}$ , match the ratios in column-I to the numbers in column-II.

List-I

(P)

\frac{v _{1}}{v _{2}}

(Q)

\frac{L _{1}}{L _{2}}

(R)

\frac{K _{1}}{K _{2}}

(S)

\frac{T _{1}}{T _{2}}

List-II

(1)

\frac{1}{8}

(2)

1

(3)

2

(4)

8

JEE Main 2002

LEVELJEE Main

A geostationary satellite orbits around the earth in a circular orbit of radius $36, 000 km$ . Then, the time period of a spy satellite orbiting a few hundred km above the earth's surface ( $R_{e} = 6400 km$ ) will approximately be

(A)

\frac{1}{2} h

(B)

1 h

(C)

2 h

(D)

4 h

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

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The planet Mars has two Moons, if one of them has a period 7 h, 30 min and an orbital radius of 9.0×103 km. Find the mass of Mars. [Take, G4π2​=6×1011 N−1m−2kg2]

If suddenly the gravitational force of attraction between earth and a satellite revolving around it becomes zero, then the satellite will

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } 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?

Assertion: An astronaut in an orbiting space station above the earth experiences weightlessness. Reason: An object moving around the earth under the influence of earth's gravitational force is in a state of 'free-fall'.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A double star system consists of two stars A and B which have time periods TA​ and TB​. Radius RA​ and RB​ and mass MA​ and MB​. Choose the correct option.

List-I

List-II

The planet Mars has two Moons, if one of them has a period 7 h, 30 min and an orbital radius of $9.0 \times 1 0^{3}$ km. Find the mass of Mars. $[Take, \frac{4 π ^{2}}{G} = 6 \times 1 0^{11} N^{- 1} m^{- 2} kg^{2}]$

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 $2 R$ ?

A double star system consists of two stars $A$ and $B$ which have time periods $T_{A}$ and $T_{B}$ . Radius $R_{A}$ and $R_{B}$ and mass $M_{A}$ and $M_{B}$ . Choose the correct option.