Elliptical Orbits and Kepler's Laws

Q.

The distance of a planet from the sun is 5 times the distance between the earth and the sun. The time period of revolution of the planet is

1. 

2. 

3. 

4. 

Q.

The average distance between the Mercury and Neptune is 29.7 AU. Express this distance in kilometers.

Q.

Two-point masses each equal to $1$kg attract one another with a force of ${10}^{-10}N$. The distance between the two-point masses is $(G=6.6\times {10}^{-11}MKSunits)$

1. $8cm$

2. $0.8cm$

3. $80cm$

4. $0.08cm$

Q.

The time period of Jupiter is $11.6years.$. How far is Jupiter from the Sun? The distance of the earth from the sun is $1.5x{10}^{11}m$.

Q. According to Kepler's Law, the orbit of the planet around the Sun is .

1. parabolic
2. circular
3. elliptical

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

1. $C$
   
2. $A$
3. $D$
4. $B$
   

Q.

Mathematically, Kepler's third law can be represented as $F=ma$.

1. True

2. False

Q. If the Earth is treated as a sphere of radius r and mass m its angular momentum about the axis of its rotation with period t is

Q.

The radius vector drawn from the sun to a planet sweeps out ________ areas in equal time.

1. Lesser

2. Greater

3. Unequal

4. Equal

Q. The following figure shows the elliptical path of a planet around the sun at point $O$. $AOB$ and $COD$ have equal areas. Suppose $t_1$ and $t_2$ be the time taken by the planet to go from $A$ to $B$ and from $D$ to $C$ respectively. Choose the correct option.​​​​​​​

1. $t_1<t_2$
2. $t_1>t_2$
3. $t_1=t_2$
4. $t_1\ne t_2$

Q.

What did Kepler prove?

Q.

Name the scientist who gave the three laws of planetary motion.

Q.

NAME THE FOLLOWING:

The scientist who gave the law of planetary motion.

Q.

Energy is produced in the sun due to ___.

1. None of these

2. Ursa major

3. Orion

4. Cassiopeia

Q. Newton's inverse square law is deduced from Kepler's ____ of planetary motion.

Q. According to Kepler's Law, the orbit of the planet around the Sun is .

1. circular
2. elliptical
3. parabolic

Q. Match the Column I with Column II

Column I	Column II
(A) Kepler's first law	(p) $T^2\propto a^3$
(B) Kepler's second law	(q) Inverse square law
(C) Kepler's third law	(r) Orbit of planet is elliptical
(D) Newton's law of gravitation	(s) Law of conservation of angular momentum

1. A-p, B-q, C-r, D-s
2. A-r, B-s, C-p, D-q
3. A-s, B-p, C-q, D-s
4. A-s, B-p, C-q, D-r

Q.

If the distance between the Earth and the Sun were half its present value, the approximate number of days in a year on the Earth would have been:

1. $64.5days$

2. $129days$

3. $182.5days$

4. $730days$

Q. The speed of the planet at the perihelion P in the figure is $v_P$ and the sun-planet distance SP is $r_P$. Relate ($r_P,v_P$) to the corresponding quantities ($r_A,v_A$) at the aphelion A. Will the planet take equal time to traverse BAC and CPB?

Q. A body of mass m is placed on a rough disk of radius R which is rotating about its own axis. Its initial angular speed zero and angular acceleration is alfa. Find out the maximum angular speed show that the body will be at rest with respect to disk.

Q.

what is the heliocentric theory of solar system?

Q. The ratio of kinetic energy of a planet at perigee and apogee during its motion around the sun in elliptical orbit of eccentricity e is

Q. The distance of a planet from the sun is $5$ times the distance between the earth and the sun. The Time period of the planet is:

1. $5^{\frac{3}{2}}years$
2. $5^{\frac{2}{3}}years$
3. $5^{\frac{1}{2}}years$
4. $5^{\frac{1}{3}}years$

Q. Figure shows the elliptical path of a planet about the sun. The two shaded parts have equal area. If $t_1$ and $t_2$ be the time taken by the planet to go from $a$ to $b$ and from $c$ to $d$ respectively.

1. $t_1<t_2$
2. $t_1=t_2$
3. $t_1>t_2$
4. Insufficient information to deduce the relation between $t_1$ and $t_2$

Q. As a planet orbits the Sun identify which of the following quantity most remain constant?

1. gravitational force
2. radius of orbit
3. angular momentum
4. velocity
5. the product of mass and velocity

Q. Kepler's third law states that square of period of revolution $\left(T\right)$ of a planet around the sun, is proportional to third power of average distance $r$ between sun and planet i.e. $T^2=K{r}^3$ here $K$ is constant. If the masses of sun and planet are $M$ and $m$ respectively then as per Newton's law of gravitation force of attraction between them is $F=\frac{GMm}{2}$, here $G$ is gravitational constant. The relation between $G$ and $K$ is described as

1. $GMK=4{\pi }^2$
2. $K=G$
3. $K=\frac{1}{G}$
4. $GK=4{\pi }^2$

Q. If the law of gravitation , instead of being inverse-square law, becomes an inverse cube law :

1. Projectile motion of some thrown by hand on the surface of the earth will be approximately parabolic
2. there will be no gravitational force inside a spherical shell of uniform density.
3. Planets will not have elliptic orbits
4. Circular orbits of planets is not possible

Q.

State Kepler's laws of planetary motion.

Q.

According to Kelper's 3rd Law, the square of the time period is proportional to the ________ power of the semi major axis of the ellipse.

1. 5th

2. 3rd

3. 4th

4. 2nd

Q. The following figure shows the elliptical path of a planet about the Sun. The two shaded parts, $S1$ and $S2$, have equal areas. If $t_1$ and $t_2$ be the time taken by the planet to go from $A$ to $B$ and from $C$ to $D$ respectively, then:

1. $t_1>t_2$
2. $t_1<t_2$
3. $t_1=t_2$
4. $t_1$ and $t_2$ cannot be compared.