Kepler's Laws of Planetary Motion

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JEE Main 2021, 18 March Shift-II

The angular momentum of a planet of mass $M$ moving around the Sun in an elliptical orbit is $L$ . The magnitude of the areal velocity of the planet is

\frac{4 L}{M}

(B)

\frac{L}{M}

(C)

\frac{2 L}{M}

(D)

\frac{L}{2 M}

JEE Main 2019, 9 Jan Shift-I

LEVELJEE Main

If the angular momentum of a planet of mass $m$ , moving around sun in a circular orbit is $L$ about the centre of the sun, its areal velocity is

(A)

\frac{4 L}{m}

(B)

\frac{2 L}{m}

(C)

\frac{L}{2 m}

(D)

\frac{L}{m}

JEE Main 2021, 26 Feb Shift-I

LEVELJEE Main

A planet revolving in elliptical orbit has I. a constant velocity of revolution II. has the least velocity when it is nearest to the Sun III. its areal velocity is directly proportional to its velocity IV. areal velocity is inversely proportional to its velocity. V. to follow a trajectory such that the areal velocity is constant. Choose the correct answer from the options given below.

The time period of a satellite of earth is $5 h$ . If the separation between the earth and the satellite is increased to $4$ times the previous value, the new time period will become

(A)

10 h

(B)

80 h

(C)

40 h

(D)

20 h

JEE Main 2021, 20 July Shift-II

LEVELJEE Main

A satellite is launched into a circular orbit of radius $R$ around Earth, while a second satellite is launched into a circular orbit of radius $1.02 R$ . The percentage difference in the time periods of the two satellites is

JEE Main 2021, 18 March Shift-I

LEVELJEE Main

The time period of a satellite in a circular orbit of radius $R$ is $T$ . The period of another satellite in a circular orbit of radius $9 R$ is

(A)

9 T

(B)

27 T

(C)

12 T

(D)

3 T

JEE Main 2021, 16 March Shift-I

LEVELJEE Main

The maximum and minimum distance of a comet from the Sun are $1.6 \times 1 0^{12}$ m and $8.0 \times 1 0^{10}$ m, respectively. If the speed of the comet at the nearest point is $6 \times 1 0^{4} ms^{- 1}$ , then the speed at the farthest point is

(A)

1.5 \times 1 0^{3} m/s

(B)

6.0 \times 1 0^{3} m/s

(C)

3.0 \times 1 0^{3} m/s

(D)

4.5 \times 1 0^{3} m/s

LEVELJEE Main

Suppose the gravitational force varies inversely as the nth power of distance. Then, the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to

(A)

R^{(\frac{n + 1}{2})}

(B)

R^{(\frac{n - 1}{2})}

(C)

R^{n}

(D)

R^{(\frac{n - 2}{2})}

JEE Main 2021, 17 March Shift-II

LEVELJEE Main

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 ............ . $P$ has the time period of 24 h.

(A)

62

(B)

6/ 2

(C)

3

(D)

5

JEE Advanced 1989

LEVELJEE Main

Imagine a light planet revolving around a very massive star in a circular orbit of radius $R$ with a period of revolution $T$ . If the gravitational force of attraction between the planet and the star is proportional to $R^{- 5/2}$ , then

(A)

T^{2}

is proportional to

R^{2}

(B)

T^{2}

is proportional to

R^{7/2}

(C)

T^{2}

is proportional to

R^{3/2}

(D)

T^{2}

is proportional to

R^{3.75}

JEE Main 1985

LEVELJEE Main

According to Kepler’s second law, the radius vector to a planet from the sun sweeps out equal areas in equal intervals of time. This law is a consequence of the conservation of _________.

JEE Advanced 1996

LEVELJEE Main

If the distance between the earth and the sun were half its present value, the number of days in a year would have been

The ratio of earth's orbital angular momentum (about the sun) to its mass is $4.4 \times 1 0^{15} m^{2} / s$ . The area enclosed by earth's orbit is approximately ......... $m^{2}$ .

JEE Advanced 2021

LEVELJEE Main

The distance between two stars of masses $3 M_{S}$ and $6 M_{S}$ is $9 R$ . Here $R$ is the mean distance between the centers of the Earth and the Sun, and $M_{S}$ is the mass of the Sun. The two stars orbit around their common center of mass in circular orbits with period $n T$ , where $T$ is the period of Earth's revolution around the Sun. The value of $n$ is _______.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The angular momentum of a planet of mass M moving around the Sun in an elliptical orbit is L. The magnitude of the areal velocity of the planet is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the angular momentum of a planet of mass m, moving around sun in a circular orbit is L about the centre of the sun, its areal velocity is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The time period of a satellite in a circular orbit of radius R is T. The period of another satellite in a circular orbit of radius 9R is

According to Kepler’s second law, the radius vector to a planet from the sun sweeps out equal areas in equal intervals of time. This law is a consequence of the conservation of _________.

If the distance between the earth and the sun were half its present value, the number of days in a year would have been

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The ratio of earth's orbital angular momentum (about the sun) to its mass is 4.4×1015 m2/s. The area enclosed by earth's orbit is approximately ......... m2.

The angular momentum of a planet of mass $M$ moving around the Sun in an elliptical orbit is $L$ . The magnitude of the areal velocity of the planet is

If the angular momentum of a planet of mass $m$ , moving around sun in a circular orbit is $L$ about the centre of the sun, its areal velocity is

The time period of a satellite in a circular orbit of radius $R$ is $T$ . The period of another satellite in a circular orbit of radius $9 R$ is

The ratio of earth's orbital angular momentum (about the sun) to its mass is $4.4 \times 1 0^{15} m^{2} / s$ . The area enclosed by earth's orbit is approximately ......... $m^{2}$ .