#36: Jumping Ship

The Question

Micah Says:
May 21st, 2005 at 7:03 am


Two Planets, made from a homogenous material, with similar average density to earth, and similar diameter, thus similar gavitational pull

Average man, standing on planet A wishes to jump and land on planet B

Neglecting all “You cant do that!” and “thats not possible!”’s

How close, in meters, do the surfaces of the two planets have to be?

And just to be fair, what about a 5th percentile Female?

The Answer

This comes down to a very simple question. Since we are disregarding all the “You can’t do that!” and “that’s not possible” comments, the simple question is, what is the height that an average man can jump?

First, we need to name Average Man. I think Average Man should be named Wilbur.

Research shows that average is somewhere between 40 cm and 50 cm. Let’s say 45 cm for the sake of argument.

If we think on this, what we really need is for Wilbur to escape the gravity well of Planet A, and enter that of Planet B. And, given our situation, this means that Wilbur needs to get to the point where the gravity of Planet A is overwhelmed by the gravity of Planet B.

In other words, the halfway point between the two planets.

So, assuming that Wilbur, as an average man, jumps 45 cm high, then (assuming that Wilbur is also homogenous and has the same density throughout), 45 cm plus half of Wilbur’s height must be the halfway point between the two planets. At the top of his jump, Wilbur lets out a girlish shriek of delight as he leaves the gravity well of Planet A and is pulled down to Planet B.

Since Wilbur is exceptionally average, he must hail from an extremely average nation. Since that phrase is an oxymoron, let’s pick one at random. How about Canada? Wilbur is an average Canadian, and he therefore is averagely 177 cm tall. Half of that is 88.5 cm.

45 + 88.5 = 133.5 cm

The distance between Planet A and Planet B must then be just under 133.5 cm, or 1.335 meters. Plenty of room for Wilbur to jump straight up and land on his head on Planet B.

The 5th percentile female (I assume 5th percentile in jumping ability as well as height), on the other hand, is likely in the “Very Poor” range of jumping ability, and can probably only jump 10 cm, and is approximately 150 cm tall. So, 95 cm or .95 meters apart. Her name is Phyllis, and she is uncomfortably crouched in the gap between the two planets.

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