Question

1. An imaginary planet has a mass twice as great as the Earth’s (5.97 x 10^24 kg), but the same radius (6.38 x 10^6 m).

   1. What is the acceleration due to gravity on the surface of the planet?

   2. What would be the weight of a 60 - kg robot on that planet?

   3. At what altitude (height from the surface of that planet) would a 60-kg person weigh 300 N?

1. 4. The period of rotation of this planet is 20 hours. At what altitude would you launch a satellite to be in geosynchronous with the planet rotation?

   5. What would be the orbital speed of that satellite?

Answer 1

Mass of the Planet, M = 2 x  5.97 x 10^24 = 11.94 x 10^24 kg

Radius of the Planet R = 6.38 x 10^6 m

Universal Gravitational Constant , G =  6.67 × 10-11 Nm^2/kg^2

(a)

Acceleration due to gravity is given by,   

(b)

Weight,

(c)

Given Weight,

Variation of with height is given by

Substituting,   

(d)

Altitude of Geo synchronous satellite from the centre of planet is given by,

  

Given Time Period of Rotation, T = 20 h = 20 x 60 x 60 = 72000 s

  

Altitude : = 47113475.09 - 6380000 = 40733475.09 m = 40733.475 km

(e)

Velocity of satellite,