## Gravitation

# Escape Velocity and Satellites

- Escape velocity is the minimum velocity of an object to escape from the gravitational field.
- Escape velocity depends up on the mass and radius of planet.
- Escape velocity is independent of the mass of the body and the direction of projection.
- There is no atmosphere on the surface of the noon because r.m.s velocity of the air molecules is greater than the escape velocity on the noon.
- If the speed of the orbital satellite is made \sqrt{2} times or increased by 41.4%
- If the orbital satellites kinetic energy is doubled then it will escape to infinity.
- Orbital velocity is the minimum velocity required by a satellite to revolve in a particular orbit.
- The direction of orbital velocity is always tangential to the orbit.
- Orbital velocity is independent of the mass of the orbiting body.
- Orbital velocity depends on mass of the planet and radius of the orbit.
- For a satellite with increase in height of the orbit from the surface of the planet then its potential energy increases kinetic energy decrease.
- Orbital velocity decreases when a satellites height is increases
- Total energy and period of revolution increases when a satellite height is increase.
- Time period of Geostationary satellite around earth is 24 hours.
- Relative velocity of Geostationary satellite is ‘O’
- Geostationary satellite parking orbit is 42, 400 km from centre of earth.
- A satellite whose orbital plane is perpendicular to equatorial plane is called polar satellite.
- Time period of polar satellite is 100 minutes.
- The angle between the equatorial plane and the orbital plane of polar satellite is 90°.
- If acceleration due to gravity is less than “Rw
^{2}” object flies off from the surface of planet - If acceleration due to gravity is greater than ‘Rw
^{2}” object will remain struck to sustain of planet - A geostationary satellite revolves from west to east in the equatorial plane.

### View the Topic in this video From 0:02 To 18:29

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1. Escape velocity of any object v_{e}=\sqrt{\frac{2GM}{R}}

2. Binding energy of the satellite of mass m is given by \tt BE=+\frac{GMm}{2r}

3. Relation between escape velocity and orbital velocity of the satellite v_{e}=\sqrt{2}\ v_{0}

4. Orbital velocity of a satellite is given by v_{0}=\sqrt{\frac{GM}{r}}=R\sqrt{\frac{g}{R+h}}

5. If satellite is revolving near the earth's surface, then r = (R + h) ≈ R Now orbital velocity, v_{0}=\sqrt{gR}\approx7.92\ km/h

6. Time period of satellite \tt T=2\pi\sqrt{\frac{r^{3}}{GM}}=\frac{2\pi}{R}\sqrt{\frac{\left(R+h\right)^3}{g}}\ \left[\because g=\frac{GM}{R^{2}}\right]

7. Near the earth surface, time period of the satellite \tt T=2\pi\sqrt{\frac{R}{g}}

8. Geostationary or Parking Satellites:

Angular velocity = \tt \frac{2\pi}{24}=\frac{\pi}{12}rad/h

9. Polar satellites:

Angular velocity = \tt \frac{2\pi}{84}=\frac{\pi}{42}\ rad/min

10.Total energy of a satellite E = KE + PE = \frac{GM\ m}{2r}\ +\left(-\frac{GM\ m}{r}\right)=-\frac{GM\ m}{2r}