Question

The escape velocity for a planet is v_e. A particle is projected from its surface with a speed v. For this particle to move as a satellite around the planet,

• A. < v <v_e
• B. < v <v_e
• C. v_e< v <$\sqrt { 2 }$v_e
• D. < v <

Answer 1

Answer: (B)

< v <v_e

Answer 2

For a satellite orbiting very close to the earth’s surface, the orbital velocity = $\sqrt { \operatorname { Rg } }$ ( mg = mv²/R). This is equal to the velocity of projection and is the minimum velocity required to go into orbit. Also, the satellite would escape completely and not go into orbit for v ≥ v_e.

⇒ v_e/√2 < v < v_e.