Exploring surface gravity: Jumping on other Worlds

Background:

Newton's law of Universal Gravitation tells us that the acceleration due to gravity g on the surface of a spherical object of mass M, radius R is:

g = GM/R2.

In that gravity field, small jumps near the surface with launch speed v will send you up to a height

h = v2/2g,

and your "hang time" off the ground will be
t = 2v/g.

Exercise:

This applet allows you to simulate jumping on a number of solar system objects, from the Sun (not recommended!) to Ceres, the largest asteroid. First, to find out how high you can jump on Earth:
  1. Stand next to a wall, and make a mark on it with a pencil as high as you can reach (without taking your feet off the ground).
  2. After one or two practice jumps, jump up and make a pencil mark on the wall as high as you can.
  3. Measure the distance between the two marks with a meter stick - This is how high you can jump on Earth.

Input the value of your vertical jump (in meter) on Earth, then select the solar system object of your choice to learn how high you would be able to jump there.

 
For information on additional objects, see Wikipedia's list of solar system objects ordered by surface gravity
Credits: Original concept: Siobhahn Morgan, modified by Philip Blanco, real-time animation by KindCoder. Animation artwork by ARG!.




On iphone, enter the name of the Sun solar system object (Mercury, Venus, Earth, Moon, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto, Eris, Ceres) and click "Done"






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