# Physics : Gravitation -2

## Kepler’s Laws of Planetary motion

– Every planet revolve around the sun in elliptical orbit and sun is at its one focus.__Law of orbit__

: – A planet moves round the sun in such a way that its areal velocity always remains constant.__Law of Areal Velocity__

Area of ABM = Area of CDM = Area of EFM

is the state at which area “ i ” sweat out by a particle as it moves along a curve__Areal velocity__- Second law can also defined as –

“The line joining the sun and the planet sweeps out equal areas in equal times.

**Law of period:**– A planet moves round the sun in such a way that the square of its period is proportional to the cube of semi major axis of its elliptical orbit.

**Escape Velocity (Ve)**

It is the minimum velocity with which a body has to be projected vertically upwards from the earth, so that it just crosses the earth’s gravitational field and never returns.

Escape Velocity__Did you know?__

- Escape velocity does not depends on mass, shape and size of the body.
- I is also called second cosmic velocity
- Escape velocity of earth = 11.2 km/s
- Escape velocity of Moon = 2.4 km/s

** Satellite:-** Satellites are natural or artificial bodies revolving around a planet under its gravitational attraction.

- Moon is the natural satellite, while INSAT-1B is an artificial satellite of earth.

__Orbital velocity of a satellite__

- It is the minimum velocity required to place or maintain satellite into a given orbit around earth.

Where, M = Mass of the planet

r = Radius of the Planet

H = height of the satellite from planet’s surface.

Planet’s surface.

**Previous year important questions**

**Q.1 What is the approximate height of any geostationary satellite from earth’s surface?**

(a) 36000 km (b) 45000 km (c) 50000 km (d) 25000 km

**Ans. (a)** Geostationary satellite is placed in the orbit which is at an altitude of 36000 km (Approximately) above mean sea level.

**Q.2 The spoon dropped by an astronaut in a satellite will –**

(a) Fall to the floor

(b) Remain stationary

(c) Continue to follow the motion of the satellite

(d) Move tangentially away.

**Ans. (c) ** Since, the spoon is inside the satellite it will acquire the velocity of satellite hence, on dropping, it will keep moving with the satellite velocity.

**Q.3 What is the minimum escape velocity of rocket to be launched into space? **

(a) 5 km/sec (b) 6 km/sec (c) 11 km/sec (d) 15 km/sec.

**Ans. (c) **

**Q.4 If the orbit of a planet is an ellipse then what is the point at which the sun is located called?**

(a) Centre (b) Circum centre (c) In centre (d) Focus

**Ans. (d)** Due to the force of gravity, planet trace out an ellipse in space as they orbit around the sun which is located at a single focus.