## Keplers Laws of Planetary Motion

Category : 9th Class

### Kepler’s laws of planetary motion

Kepler observed that different planets take different time to complete one revolution around the sun. From s this observation of planetary motion he deduced that square of time period is proportional to the cube ob its distance from the sun.

Kepler’s First Laws

Kepler’s first laws of planetary motion states that planets move around the sun in such a way that sun always remains at one of its focus.

Kepler’s second law

According to second law the line joining planet to the sun sweeps out equal area in equal time interval, as the planet revolve around the sun in a elliptical orbit.

Kepler's Third Law

It states that square of time period is proportional to the cube of its semi major axis.

Let A and B be the two planets whose time period are ${{T}_{1}}$ and ${{T}_{2}}$. If ${{r}_{1}}$ and ${{r}_{2}}$ be their distance from the sun/then

$\frac{{{T}_{1}}^{2}}{{{T}_{2}}^{2}}=\frac{{{r}_{1}}^{3}}{{{r}_{2}}^{3}}$

Orbital Velocity

The velocity required for an object to revolve around the planet in its orbit is called its orbital velocity. The orbital velocity of the earth is given by $V=\sqrt{g{{R}_{e}}}$.

Its numerical value is 7.92 km/sec. The orbital velocity is independent of the mass of the object. If the velocity is less than orbital velocity, then the object will fall back on the earth and if the velocity is more than the orbital velocity, then it will get lost into the space.

Escape Velocity

The minimum velocity with which an object must be projected so that it escapes the gravitational pull of the earth is called the escape velocity.

It is given by ${{V}_{e}}=\sqrt{2g{{R}_{e}}}$ . The numerical value is 11.2 km/sec.

Find the weight of the object on the surface of moon whose weight on the surface of earth is 9.8 N,

(a) 2.2 N

(b) 1.63 N

(c) 3.2 N

(d) 4.1 N

(e) None of these

We know that escape velocity of earth is 11.2 km/s. Find the escape velocity of planet whose radius and mass is twice that of earth.

(a) 11.2 km/s

(b) 22.4 km/s

(c) 11.272 km/s

(d) 33.6 km/s

(e) None of these

A body whose weight is 120 kg on the earth. Find its weight on the surface of moon.

(a) 10kg

(b) 15kg

(c) 20kg

(d) 25kg

(e) None of these

The orbital velocity of the earth is;

(a) 7.2 km/s

(b) 7.56 km/s

(c) 7.84 km/s

(d) 7.92 km/s

(e) None of these