Math/physics people -- help me out!

[InternalDialogue]

This is a friend of mine. He has written several huge Hollywood successes.

Here's a chance to maybe have a chance at influencing a future blockbuster.

http://johnaugust.com/archives/2010/math-advice-for-paranoid-aliens

Story problems in math rarely overlap with story problems in screenwriting, but today I have one that I could use some help figuring out.

Far away on a distant planet, an intelligent but very paranoid species is constructing a series of terrestrial watchtowers to scan the heavens, making sure no space-traveling enemies sneak up on them

[RandomThoughts]

1. Depends on if you want to scan both near and far.

Since at some point there is overlap that is a ratio to planet size and distance at overlap.

At 180 degrees, each viewing arc is a tangent on a circle in 2d.

Which would mean terrestrial you would need infinite amount of units to cover every area, but only if you also wanted 1/infinate inch above the ground also watched. So from a math perspective it is the old story of plane tangents on a sphere, where the further you go out at point of first intersection the fewer you would need.

The easy answer would be to think of a cube and just say six.

But basically any two that are not parallel would intersect, and at that point of intersection that area would have full coverage. So three on a circle would give full coverage, but on a sphere in 3d coverage would requier another level, or one or two more, would have to think about it to know if it is 4 or 5 for max coverage.


Interestingly with 181 degree coverage, an not on surface, 2 would give full coverage, but the range of overlap would be based on distance apart the two units are.





However you remind me of a great SG1 story, where Daniel Jackson was given great abilities, and it turned him evil.

Which is a huge thought on what happens when people think they can do stuff without consequence, or without limits, corruption often occurs.

That episode was a 'destroy ring of power episode' where the child told him that if he had Gould power it would only end up making him bad, since bad only can do bad, and in that episode the knowledge was bad.

Or power corrupts, hence why the less corruption you let in, the more power things try and make you think you have, to get you to think you are more then you are, and why I contently laugh about how I don't do things, nor think I have any control over other people, but believe people make free will choices. Although I do think both good and bad powerful things can occur through people, or it seems that way.

I think people should be free, and would not ever steal free will.


Although I still will have the finances to go out and have beers with friends and travel, because by all justice I already have it even if not here.

[MajorChode]

3. Why wouldn't a tetrahedron do it?

You only need to build planes of coverage such that if an object breaks one of the planes, you know something is coming.

So if you had 4 sensors that had sufficient range to form a tetrahedron around the planet, it seems as if you would have complete coverage.

[RandomThoughts]

4. The plane is to visualize the coverage area.

The plane itself is not the coverage area.

The plane, and everything on the opposite side of the planet of the plane is the coverage area.

So something would not have to break the plane, but planes would have to intersect to get coverage.

So not sure what you mean by something breaking the plane to get detection.

Have to look up tetrahedron again, will look that up later.

[MajorChode]

6. That's who the US radar defense network works

At least that's how the long range detection system works (if you don't count the short range radar network around the border).

There isn't a coverage area, per se, only a 2 dimensional plane of detection sort of like a fence. If something penetrates that fence, they know it is there and heading in the direction of the US.

A tetrahedron is a polygon with the least amount of sides, so it would require the least amount of sensors to build each side.

[pokerfan]

2. two, in theory

If each tower can really see half the sky, down to the horizon. It does leave a gap the thickness of the planet extending outward indefinitely. But, since we're talking towers, perhaps each one can "see" a little more than 180 degrees of the sky so that at some distance from the planet there would be overlap. Otherwise, any of the platonic solids would work, a tetrahedron (four equally spaced towers or satellites) being the most minimal.

[rug]

5. Since when are Republicans in space?

[applegrove]

7. LOL!