Question

10) State and explain kepler's
low of planetary motion Name
the physical quantities which
remain constant During the
planetary motion . If the
Distance Between the earth and
the sun wal half its
present value then and the
no. of days in a year​

Answer 1

Explanation:

A planet moves around the sun in an elliptical orbit with the sun at one of its foci. The physical quantity associated with the motion of the planet that remains constant with time is: velocity. Centripetal force.

Answer 2

Kepler's Law of Planetary Motions:

There are three Kepler's  law of planetary motion. They are based on Orbits, Periods and Areas.

Kepler's Law of Orbits:

The planets move in elliptical orbital around the sun with sun in one of its foci.

Kepler's Law of Periods:

The square value of the time period of planet is equal to the cube of the semimajor axis of the ellipse.

Kepler's Law of Areas:

The line joining the sun and planet is equal area in equal interval of time.

Physical quantities which  remain constant:

The gravitational constant remains same.

Distance Between the earth and  the sun:

From, Kepler's Law of Periods,

$T^{2} \propto R^{3}$

$\frac{T_{1}^{2}}{T_{2}^{2}}=\frac{R_{1}^{3}}{R_{2}^{3}}$

$\frac{T_{1}^{2}}{T_{2}^{2}}=\frac{8 R^{3}}{R_{1}^{3}}$

$\frac{T_{1}^{2}}{T_{2}^{2}}=8$

$\left(\frac{T_{1}}{T_{2}}\right)^{3}=8$

From question, the number of days in a year is asked, thus,

$T_{2}=\frac{365}{2 \sqrt{2}}$

$\therefore T_{2}=129 \ days$