The GATE Grind

GATE 2020 AE – Question 21

Flight Mechanics & Space Dynamics · Space dynamics: central force motion, Keplerian orbits, Kepler's laws and escape velocity · 1 mark · Multiple choice

A satellite of mass m has speed V at distance r from Earth’s centre. G is the gravitational constant and M is Earth’s mass. For a hyperbolic trajectory, which holds?

  1. $mV^2/2>GMm/r$
  2. $mV^2/2<GMm/r$
  3. $mV^2/2=GMm/r$
  4. $mV^2/2<2GMm/r$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) $mV^2/2>GMm/r$

Explanation

Hyperbolic Kepler motion has positive total orbital energy. Thus $E=mV^2/2-GMm/r>0$, which gives A. Zero energy is the parabolic escape boundary; negative energy corresponds to a bound ellipse.

More Space dynamics: central force motion, Keplerian orbits, Kepler's laws and escape velocity questions

All Space dynamics: central force motion, Keplerian orbits, Kepler's laws and escape velocity questions →