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### Trigonometry and Space Exploration

```Date: 05/29/2002 at 13:21:07
From: Jim
Subject: Trigonometry and space exploration?

How does Trigonometry relate to space exploration? I understand
that angles are needed to be figured out. But for what?
```

```
Date: 05/29/2002 at 16:40:14
From: Doctor Ian
Subject: Re: Trigonometry and space exploration?

Hi Jim,

Here's a real life example, from when I worked at NASA.  Suppose
Voyager is cruising towards Jupiter, and you tell it to snap a
picture that shows Io and Europa (two of its moons) in the same
frame.

Now, this defines a triangle, with the spacecraft, Io, and Europa
at the corners.  What you want to know is:  How far is the
spacecraft from the moons?  What you've observed is an angular
separation between the moons, and your models of the solar system
can tell you the linear separation between them.  So you want to
use that information to find the size of the triangle.

Other examples would include wanting to know the angle at which
sunlight is falling on a surface that you've taken a picture of;
knowing the angle between the velocity of a spacecraft and the
magnetic field of a planet; and so on.

Basically, when you explore space, you send robots out to take
all kinds of measurements; and afterwards, in order to figure out
what the measurements _mean_, you have to compute all kinds of
angles and distances, so you can compare what actually _happened_
against what you _predicted_.  Doing the math is what
distinguishes science from tourism.  :^D

Does this help?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
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