IIT (NTSE/Olympiad)  

Gravitation

Geo Stationary Satellite


(a) Such satellites which are stationary with respect to an observer on earth are termed as Geostationarysatellites. they are also called Parking satellites.
(b) The direction of rotation of geo-stationary satellites is from west to east, the time period is 24 hours and its angular velocity is same as that of axial velocity of earth, revolving around its axis.
(c) Geo-stationary satellites can be launched just above the equator.
(d) The radius of orbit of Geo-stationary satellite is r = 42,000 km and its height above the surface of earth is h = 36, 000 km.
(e) Different values of satellite -
1) Angular Velocity (w) = 7.1 x 10-5rad/sec
2) Linear Velocity (v) = 3.1 km/sec.
3) Time Period (T) = 24 hours.
d) Height above the earth's surface (h) = 36,000km (approx.)
(f) At time t, the angular displacement of earth and Geo stationary satellite is same.
(g) Angular momentum of satellite is conserved and it is equal to

(h) Satellites behaves like freely falling bodies towards planet.
(i) The satellite revolves around the earth in an orbit with earth as centre or a focus.
(j)If a packet is released form the satellite, it will not fall on the earth but will remain revolving in the same orbit with the same speed as the satellite.
(k) No gravitational force of satellite is used up for providing necessary centripetal force. Due to gravitational force the effective value of acceleration due to gravity becomes geff = 0, as a result effective weight becomes weff = 0, so the man sitting in the satellite enjoys weightlessens. Man experiences this weightlessness condition only when weight of satellite is very less therefore gravitational effect of satellite is negligible.
Although moon is also a satellite of the earth, but a person on moon does not feel weightlessness. Thereason is that the moon has a large mass and exerts a gravitational force on the person (and this is the weight of the person on the moon). On the other hand, the artificial satellite having a smaller mass does not exert gravitationalforce on the space-man.
8.1 Relation between velocity of Projection and shape of orbit
Shape of the satellite's orbit depends on its velocity.
V0 = ; orbital velocity of the satellite's
Cases :
(a) If V < V0 - In this case satellite will leave its circular orbit and finally fall to earth following spiral path.
(b) If V = V0 - In this case satellite will rotate in circular path.
(c) If V0 < V √2V0 - In this case satellite will revolve around the earth in elliptical orbit.
(d) If V = √2 V0 - In this case satellite will leave the gravitational field of earth and escape away following a parabolic path.
(e) If V > √2 V0 - In this case the satellite will escape, following a hyperbolical path.


IIT (Class X)

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