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PhysicsClassical Physics

An Astronaut Stands on the Surface of a Spherical Asteroid: Escape and Rotation Limits

For an Earth-density spherical asteroid, the astronaut can escape by jumping only if the radius is about 1.8 km or less; the cohesionless rotation limit has an 84.6-minute period.

Question

An astronaut is on the surface of a spherical asteroid of radius rr and mean density similar to that of Earth. On Earth, this astronaut can jump to a height h=0.5 mh=0.5\,\mathrm{m}. If the astronaut jumps on this asteroid, the astronaut can permanently leave the surface.

  1. Taking the radius of Earth as RE=6.4×106 mR_E=6.4\times10^6\,\mathrm{m}, find the largest radius the asteroid can have.
  2. How fast could this asteroid rotate without the astronaut being flung away from the surface?

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Evidence boundary

The calculation treats similar density as equal to Earth’s mean density and assumes the astronaut leaves the surface with the same speed as in the Earth jump. It neglects atmosphere, irregular shape, material cohesion, and launch assistance from rotation. The rotation threshold is evaluated at the equator with g_E = 9.8 m/s².