Question

Planet Roton, with a mass of 3.89 × 1024 kg and a radius of 4070 km,...

Planet Roton, with a mass of 3.89 × 1024 kg and a radius of 4070 km, gravitationally attracts a meteorite that is initially at rest relative to the planet, at a great enough distance to take as infinite. The meteorite falls toward the planet. Assuming the planet is airless, find the speed of the meteorite when it reaches the planet's surface.

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Answer #1

Given Data:

  • Mass of planet Roton:
  • The radius of planet Roton:
  • The initial velocity of meteorite wrt planet:
  • Initial separation between the planet and meteorite:

Let the speed of the meteorite when it reaches the planet's surface is and its mass is .

The separation between their centers at this instant is .

As the planet is airless and no other dissipative forces are present, we can apply the conservation of mechanical energy.

By putting the given values and value of universal gravitational constant 'G', we have:

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