Geo synchronous Orbit

Its the body or objects Orbit having an angular velocity equal to the angular velocity of the planet, around which orbit of the object or body takes place.

If a body is in circular orbit with the angular velocity equal to that of Earth and also rotates in the  same direction as that of Earth from east to west, its movement is synchronous with the rotation of earth and it is said to be Geo-Synchronous orbit.

for example :
Earth rotates from east to west on its axis and completes one rotation each day, The angular velocity of earth  can be calculated as follows

consider earth rotates on its axis once in every 24 hour, the complete circle is 360 degrees i.e   radians , so per hour earth's angular velocity is

.

so the object orbiting around earth orbit should move at an angular velocity of 15 degrees/hour to reach the Geo synchronous condition.

similarly for other planets, the Synchronous angular velocity can be calculated as follows,

angular velocity in degrees/hour

Mercury -  0.255 (mercury spins about its axis with a period 58 days approximately so 360/24x58)
Venus - 0.061 (Venus spins about its axis with a period of 243 days approx. so 360/24x243)
Earth -  15.04 (Earth spins about its axis with a period of 24 hours i.e 1 day approx. so 360/24)
Mars -  14.62 (Mars spins about its axis 24.62 hours approx. so 360/24.62)
Jupiter - 36.29 (Jupiter spins about its axis 9.92 hours approx. so 360/9.92)
Saturn - 33.77 (Saturn spins about its axis 10.66 hours approx. so 360/10.66)
Uranus - 20.88 (Uranus spins about its axis 17.24 hours approx. so 360/17.24)
Neptune - 22.34 (Neptune spins about its axis 16.11 hours approx. so 360/16.11)
Pluto - 2.34 (Pluto spins about its axis 153.3 hours approx. so 360/153.3)


In same way angular velocity in rad per second can be calculated by multiplying the denominator 24 by 3600 i.e     60 min x 60 sec so the angular velocity per sec is 7.273x10 ^ -5 rad/sec