A View from the Back of the Envelope top

Probing near space with a flashlight
Deep understanding

A flashlight generates a beam of light.
The light forms a cone, getting wider as it goes.


When you turn on the flashlight, the light cone leaps out, its front moving at 3 × 108 m/s.


In a nanosecond, it goes a foot. In a second, it zips by the moon. In 10 minutes, the sun. About the same to Mars (depending on where it and earth are in their orbits). 4/3 hour to Jupiter.
(Time versus distance.)

Your flashlight is a photon generator. You are creating lots of tiny photons in your lightbulb, and spitting them out at the universe.

What happens when you turn of the flashlight?
Well, the cone gets chopped off.

===| --++++++XXXXXXXXX...
===| ++++XXXXXXXXX...
===| XXXXX...

And if you flick the flashlight on and off...

===| --++++++XXXXXXXXX
You get a cone, with a big leading face, and a chopped off trailing base, zipping along at light speed, getting wider as it goes.
A 1 second flash with produce a 3 × 108 m long cone (~earth-moon distance).
[add a better picture]

How wide is the cone?
Well, a narrow beam flashlight might be 6 degrees (0.1 radians, so the math is easy). If it has gone 1 m, its face will be 0.1 m wide. 10 m out, 1 m wide. If it has gone 4 × 108 m (by moon), it will be 4 × 107 wide (say three earth diameters).

So you can send these hunks of light zipping off into the universe.

Then you can start waving the flashlight.
You can send off zig-zags, cirlycues, etc. [See shape caveat.]

How big is the cone as it goes by the bulge in the middle of the galaxy? Which way should you point?

Back of my envelope...

Example: Sun is 1.5 × 1011 m from earth.
1.5 × 1011 m / 3 × 108 m/s = 500 s. ~8 minutes.

Example: Jupiter is 780 × 106 km from sun (8 × 1011 m).
8 × 1011 m / 3 × 108 m/s = ~3 × 103 s ~= 3/4 hour.
Now jupiter could be on the opposite side of the sun from earth, with a flashlight delay of 3/4 hour + 8 minutes, or on the same side, as close as it gets, with 3/4 hour - 8 minutes. Its probably in between. Where is it now? There are solar system maps on the web (eg, Solar System Live).

[Shape caveat]
I was thinking that as the light dims (most of your photons havent made it), that waved shapes get more problematic to talk about than the simple cone. But as both end up being just probability distributions of where the odd photon is likely to be found, I think the waved shapes are no less valid.

I originally planned to say something about your creating photons in your lightbulb, and sending them off towards the moon, to smack into lunar dust a second or so later. Send you photons off to be absorbed by Venus's clouds, or a Martian dust storm.
But I would feel more comfortable first running the numbers on how many photons are making it. I dont really care about the detectability of the signal, (though that could make a fun information theory exercise), I just want to have a feel for the magnitude.
Also, I'm puzzled - if a wavefront is say as wide as the moon, and energetically there is only a single photon arriving, what can one say about where it hits?
(Oops - and as my understanding of light improves a little... the use of "photon" in this context is perhaps(?) unfortunate. At these classical scales, a strictly wave description is more appropriate.)

There is A Solar System Scale Model Meta Page.

A View from the Back of the Envelope
Comments encouraged. - Mitchell N Charity <mcharity@lcs.mit.edu>

 Photons and waves and detection, oh my.

 1999.Apr.21   Reader suggests saying "photon" is fine, for some interpretation.
               So I caveated my caveat, and added a note on my puzzlement.
 1998.Aug.18   Added links to `Solar System Live' and `Model Meta Page'.
               Thanks to a reader for the suggestion.
 1997.Sep.19   Added `wave not photon' caveat.
 Long ago      Created.