Kepler's Law of Planetary Motion

Choose the incorrect statement from the given statements

The period of the satellite of the earth orbiting very near to the surface of the earth is $T_0$. What is the period of the geostationary satellite in terms of $T_0$

Duration of a year on a planet is $11$ times of the year on the earth. Find the distance of that planet from the sun. The earth is at distance $1.5\times {10}^8 \mathrm{km}$ from the sun.

A planet is moving in an elliptical path around the Sun. It does obey Kepler's laws of planetary motion. Read the following statements and identify the correct statements
(I) The potential energy of the planet remains same in the entire path.
(II) The kinetic energy of the planet remains same in the entire path.
(III) The total energy of the planet remains same in the entire path.
(IV) The linear momentum of the planet remains same in the entire path.
(V) The angular momentum of the planet remains same in the entire path.

Suppose two planets $A$ and $B$ revolve around a Sun in the galaxy. The semimajor axis of $A$ and $B$ are $1$ and $5\mathrm{AU}$ (astronomical unit) respectively. If the period of revolution of $A$ is $1$ year, the period of revolution of $B$ is

If a planet moving in a circular path having time period of revolution $T$ is suddenly stopped, after what time it will collapse onto the sun?

The point on the earth's orbit that is farther away from the sun is aphelion.

Kepler's second law is a consequence of

State Kepler's law of area.

Distance of a planet from the sun is constant.

State Kepler's law of orbits.

State Kepler's third law of planetary motion.

Kepler's three laws of planetary motion describe how planetary bodies orbit the _____.

A comet orbits the sun in an elliptical orbit. Which of the following is constant throughout its orbit?

If earth be at one half its present distance from the sun, how many days will there be in a year?

A hypothetical planet has density g, radius R, and surface gravitational acceleration g. If the radius of the planet were doubled, but the planetary density stayed the same, the acceleration due to gravity at the planet's surface would be:

According to the Kepler's second law, the speed of the planet is ________, when it is closest to the sun and is ________, when it is farthest from the sun.

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

If a graph is plotted between ${\mathrm{T}}^2$ and ${\mathrm{r}}^3$ for a planet, then its slope will be (where, ${\mathrm{M}}_{\mathrm{S}}$ is the mass of the sun):

Assertion:  Areal speed of planets moving around the sun remains constant.

Reason:  Gravitational force between planet and sun provides required centripetal force to the planet for revolution around the sun.