April 21^st, 2005

About six weeks ago, someone on my company's intranet pointed out that there is an upcoming World Jump Day. The idea of this -er- exercise is that if enough people jump at the right time, the Earth's orbit will be altered enough that we can move ourselves a little further from the sun and subsequently counter global warming. Yeah, right ...

So I formulated the following response and posted it on the intranet as a reply:

OK, so let's start with the obvious one: Would the mass of nearly every single person's jump have any effect at all?

1) First, let's estimate the mass of Earth's population:

I estimate that the average mass of a human is 75 Kg (and this is generous). And I further estimate that only about 5 billion humans are capable of jumping (disabled, elderly, too young, etc. trim the numbers down—again, this is generous).

So, 5,000,000,000 people X 75 Kg/person = 3.75 X 10¹¹ Kg

2) Next, let's estimate the mass of the Earth:

We already know some values:

• a: acceleration due to gravity, a = 9.8 m/s², (thank you, Galileo—you are the centre of my universe, even if the Earth isn't)
• r: the radius of the Earth, r = 6.38 x 10⁶ m, (heck, even the Greeks—Erastothenes—knew this one)
• G: the gravitational constant, G = 6.67 x 10^-11 m³ / (Kg sec²), (thanks, Sir Isaac, though I hear you were a bit freakish)

And there are some simple equations that I couldn't quite remember, so I got them off the Internet too:

• F = ^GmM / _r²

• F = ma

Now let's make these two descriptions of force equal to each other:

F = ^GmM / _r² = ma

And we get the following:

a = ^GM / _r²

Solving for M (Mass of the Earth):

M = ^ar2 / _G

Plug and sub, and we get:

M = 5.98 X 10²⁴ Kg

Wow, heavy, man.

3) Finally, let's compare the two:

The mass of the Earth is 13 orders of magnitude larger than the mass of five billion people. That is: 3.75 X 10¹¹ / 5.98 X 10²⁴ or 6.27 X 10^-14.

Written out in full, five billion people have 0.000000000627 percent of the mass of the planet they live on.

4) Therefore:

Even assuming everyone was a heavy white person, and it was possible to coordinate 5 billion people to jump at the same time, we could still all jump until we are sore in the feet, and make not even an appreciable difference in the orbit of the Earth.

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