One of the greatest ideas proposed in human history is the fact that the earth is a planet, among the other planets, that orbits the sun. Johannes Kepler discovered three empirical laws by using the data on planetary motion:

**Law of Orbits:**Each planet moves in an elliptical orbit, with the sun at one focus of the ellipse.**Law of Area:**A line joining the earth to the sun sweeps equal area in equal interval of time.**Law of Period:**The square of the periods of revolution is directly proportional to cubes of the semi-major axis.

These laws go by the name Kepler’s laws of planetary motion. It was in order to explain the origin of these laws, among other phenomena, that Newton proposed the theory of gravitation.

**Q.1. According to Kepler, planets move in**

(1) Circular orbits around the sun

(2) Elliptical orbits around the sun with sun at exact centre

(3) Straight lines with constant velocity

(4) Elliptical orbits around the sun with sun at one of its foci

## Answer

(d) Kepler’s first law,**Law of Orbits:**All planets move in elliptical orbits, with the sun at one of the foci of the ellipse.

**Q.2. The minimum and maximum distances of a planet revolving around sun are r and R. If the minimum speed of planet on its trajectory is v0, its maximum speed will be **

(a) V_{0}R/r

(b) V_{0}r/R

(c) V_{0}R^{2}/r^{2}

(d) V_{0}r^{2}/R^{2}

## Answer

(a) According to Kepler’s second law,**Law of Areas:**The line that joins any planet to the sun sweeps out equal areas in equal intervals of time. Thus planets appear to move slower when they are farther from sun than when they are nearer. Now, for planets moving around the sun in an elliptical orbit, Angular momentum is conserved.

**Q.3. A planet of mass m moves around the sun of mass M in an elliptical orbit. The maximum and minimum distances of the planet from the sun are r1 and r2 respectively. The time period of the planet is proportional to **

(a) r_{1}^{3/2}

(b) r_{2}^{3/2}

(c) (r_{1}+r_{2})^{3/2}

(d) (r_{1}-r_{2})^{3/2}

## Answer

(c)**Q.4. In a satellite if the time of revolution is T, then potential energy is proportional to **

(a) T^{1/3}

(b)T^{3 }

(c) T^{ -2/3}

(d) T^{ -4/3}

## Answer

(c)**Q.5. During motion of a planet from perihelion to aphelion the work done by gravitational force of sun on it is**

(1) Zero

(2) Negative

(3) Positive

(4) May be positive or negative

## Answer

(b)**Q.6. The period of a satellite in a circular orbit near a planet is independent of**

(a) the mass of the planet

(b) the radius of the planet

(c) the mass of the satellite

(d) All of the above

## Answer

(c)**Q.7. Which of the following is/are not a relevant statement(s) to Kepler’s laws of planetary motion?**

I. Kepler’s second law is based on law of conservation of angular momentum.

II. Every planet revolves around the sun in circular orbits with sun at the centre of the orbit.

III. Planets situated at larger distances from the sun take longer time to complete one rotation

(a) I only (b) II only

(c) II and III

(d) I, II and III

## Answer

(b) II only**Q.8. A planet is revolving around the sun as shown in elliptical path**

The correct option is

(a)** **the time taken in travelling DAB is less than that for BCD

(b) the time taken in travelling DAB is greater than that for ABC

(c) the time taken in travelling CDA is less than that for ABC

(d) the time taken in travelling CDA is greater than that for ABC

## Answer

(a)Q.9. The figure shows elliptical orbit of a planet m about the sunS. The shaded area SCD is twice the shaded area SAB. If t_{1}is the time for the planet to move from C to D and t_{2} is the time to move from A to B then

(a) t_{1} = 4t_{2} (b) t_{1} = 2t_{2}(c) t_{1} = t_{2} (d) t_{1} > t_{2}

## Answer

(b)Q.10. The planet mercury is revolving in an elliptical orbit around the sun as shown in fig. The kinetic energy of mercury will be greatest at

(a) A

(b) B

(c) C

(d) D