A satellite is taken at a height equal to the radius of the earth and then projected horizontally with a speed of 7 km/s. State the nature of its orbit. (G = 6.67 x 10-11 Nm2/kg2, Radius of the earth = 6400 km)
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r = 2R
v = 7 km/s
Orbital Velocity = Vo= √(GM/r) = √(GM/2R)
Escape Velocity = Ve = √(2GM/r) = √(2GM/2R) = √2 Vo
Vo = 5.578 km/s
Ve = 7.889 km/s
so,
Vo < v < Ve ..
hence, the path of the satellite is elliptical.
v = 7 km/s
Orbital Velocity = Vo= √(GM/r) = √(GM/2R)
Escape Velocity = Ve = √(2GM/r) = √(2GM/2R) = √2 Vo
Vo = 5.578 km/s
Ve = 7.889 km/s
so,
Vo < v < Ve ..
hence, the path of the satellite is elliptical.
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