Re: Calculating spherical surface area - how?

In TML Msg. No. 7166, Gregg Giles [email removed] writes:

>    I'm trying to determine the surface area of a hypothetical planetary body,
> given the circumference of that body (assuming it is a pefect globe with no
> blemishes or terrain). Does anyone know the formula for this? I'm working in
> kilometers, and suck at math. Please reply directly. Thank you!

This is a trivial exercise, when armed with the necessary two equations:

  1) circumference = pi * diameter
       - or -
     circumference = pi * radius * 2

and...

  2) surface area = pi * radius^2

Since you already know the circumference (c), we can calculate the
radius (r) as:

  r = c / (2 * pi)

Thus, the surface area (s) is:

  s = pi * (c / (2 * pi))^2

BTW, is doesn't matter what unit of measurement you work in (kilometers,
miles, or cubits), since the math is abstract. Whatever unit you start
with is the unit you'll get the results in.

Now what *I* want to know is how to calculate liberated energy from
a nominally non-elastic collision.  The Shoemaker-Levin (sic) comet
is going to hit Jupiter in July, and I'd like to know how many ergs
will be released when several 4-kilometer in diameter chunks of ice
slam into a nice, thick hydrogen laden atmosphere at 60 km/sec.

mark f. cook * 2055 sw whiteside dr. * corvallis, or * [email removed]
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"When your enemy falls, don't rejoice -- but don't pick him up either."
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