# Kepler's Law

## Trending Questions

**Q.**

If the earth is at one-fourth of its present distance from the sun, the duration of the year will be** **

Half the present year

One-eighth the present year

One-fourth the present year

One-sixth the present year

**Q.**

The angular momentum of a planet of mass $M$ moving around the sun in an elliptical orbit is $\overrightarrow{L}$. The magnitude of the areal velocity of the planet is

$\frac{L}{M}$

$\frac{2L}{M}$

$\frac{L}{2M}$

$\frac{4L}{M}$

**Q.**

For the planet-sun system identify the correct statement

The angular momentum of the planet is conserved

The total kinetic energy of the system is conserved

The momentum of the planet is conserved

All of the above

**Q.**

Two satellites S1_{ }and S2 revolve round a planet in coplanar circular orbits in the same sense. Their periods of revolution are 1 hour and 8 hours respectively. The radius of the orbit of S1=104km When S2 is closest to S1 find speed of S2_{ }relative to S2 and the angular speed of S1 actually observed by an astronaut at S1.

-4.91 ×10−4 rad s−1

-2.91 ×10−4 rad s−1

2.3 ×10−4 rad s−1

-6.00 ×10−8 rad s−1

**Q.**The orbit of a planet around a star is an ellipse.

- True
- False

**Q.**

Two planets of equal mass orbit a much more massive star (figure). Planet m1 moves in a circular orbit of radius 1×108 km with period 2 year. Planet m2 moves in an elliptical orbit with closest distance r1=1×108 km and farthest distance r21.8×108km, as shown. Using the fact that mean radius of an elliptical orbit is the length of the semi-major axis, find the period of m′2 s orbit.

2.1 year

3.31 year

4.12 year

5.24 year

**Q.**

Venus looks brighter than other planets because

It is heavier than other planets

It has higher density than other planets

It is closer to the earth than other planets

It has no atmosphere

**Q.**A mass of 50 kg is placed at the center of a uniform spherical shell of mass 100 kg and radius 50 m. If the gravitational potential at a point, 25 m from the center is V kg/m. The value of V is:

- −4G
- −60G
- −20G
- +2G

**Q.**The earth moves around the sun in an elliptical orbit as shown in figure. The ratio OAOB=x. The ratio of the speed of the earth at B to that at A is nearly

- √x
- x
- x√x
- x2

**Q.**Two satellites S1 and S2 revolve around a planet in coplanar circular orbits in the same sense. Their periods of revolution are 1 hour and 8 hours respectively. The radius of the orbit of S1 is 104 km. When S1 is closest to S2, the angular speed of S2 as observed by an astronaut in S1 is :

- π rad/hr
- π/3 rad/hr
- 2π rad/hr
- π/2 rad/hr

**Q.**The escape velocity for a body projected vertically upwards from the surface of earth is 11 km/s. If the body is projected at an angle of 45∘ with the vertical, the escape velocity will be

- 11√2 kms−1
- 22 kms−1
- 11 kms−1
- 11√2 kms−1

**Q.**The orbit of a planet around a star is an ellipse.

- True
- False

**Q.**The planet mercury is revolving in an elliptical orbit around the sun as shown in the figure. The kinetic energy of mercury will be greater at

- A
- B
- C
- D

**Q.**

The period of revolution of an earth satellite close to surface of earth is 90 min. The time period of another satellite in an orbit at a distance of three times the radius of earth from its surface will be

90√80min

360 min

720 min

270 min

**Q.**An earth satellite has angular momentum α and its areal velocity about earth is β, then mass of satellite is

- αβ
- α2β
- α3β
- 2αβ

**Q.**

The time period of a satellite in a circular orbit around a planet is independent of______.

the mass of the planet

the radius of the planet

the mass of the satellite

- density of the planet

**Q.**

Mass M is divided into two parts xM and (1 − x)M. For a given separation, the value of x for which the gravitational attraction between the two pieces becomes maximum is

12

35

1

2

**Q.**The earth E moves in an elliptical orbit with the Sun S at one of the foci as shown in figure. Its speed of motion will be maximum at the point

- C
- A
- B
- D

**Q.**

The distance of neptune and saturn from sun are nearly 1013 and 1012 meters respectively. Assuming that they move in circular orbits, their periodic times will be in the ratio

√10

100

10√10

1√10

**Q.**

A planet moves around the sun. At a given point P, it is closest from the sun at a distance d1 and has a speed v1. At another point Q, when it is farthest from the sun at a distance d2, its speed will be

d21v1d22

d2v1d1

d1v1d2

d22v1d21

**Q.**A satellite can be in a geostationary orbit around earth at a distance r from the center. If the angular velocity of earth about its axis doubles, a satellite can now be in a geostationary orbit around earth, if its distance from the center is

- r2
- r2√2
- r(4)1/3
- r(2)1/3

**Q.**

The period of a satellite in a circular orbit of radius R is T, the period of another satellite in a circular orbit of radius 4R is

4T

T4

8T

T8

**Q.**

The distance of neptune and saturn from sun are nearly 1013 and 1012 meters respectively. Assuming that they move in circular orbits, their periodic times will be in the ratio

√10

100

10√10

1√10

**Q.**The earth moves around the sun in an elliptical orbit as shown in figure. The ratio OAOB=x. The ratio of the speed of the earth at B to that at A is nearly

- √x
- x
- x√x
- x2

**Q.**The planet mercury is revolving in an elliptical orbit around the sun as shown in the figure. The kinetic energy of mercury will be greater at

- A
- B
- C
- D

**Q.**A comet revolves around the Sun, then which of the following is incorrect?

- Speed is greatest when comet is closest to the Sun
- In half motion, comet is retarded and in the other half motion, comet is accelerated
- Angular momentum of comet about any point is constant
- Motion is in plane

**Q.**Which of the following are true for Planetary system in the solar system

- Conservation of kinetic energy
- Conservation of linear momentum
- Conservation of angular momentum
- None of these

**Q.**

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

65

129

183

730

**Q.**Two satellites S1 and S2 revolve around a planet in coplanar circular orbits in the same sense. Their periods of revolution are 1 hour and 8 hours respectively. The radius of the orbit of S1 is 104 km. When S1 is closest to S2, the angular speed of S2 as observed by an astronaut in S1 is :

- π rad/hr
- π/3 rad/hr
- 2π rad/hr
- π/2 rad/hr

**Q.**

In planetary motion the areal velocity of position vector of a planet depends on angular velocity (ω) and the distance of the planet from sun (r). If so the correct relation for areal velocity is

dAdt∝ ω r

dAdt∝ ω2 r

dAdt∝ ω r2

dAdt∝ √ω r