Time and distance at constant C: A sieries of questions for Umbran or other physicists.

[Staffan]

Well, I was thinking of how hard it would be to hit a small target moving at .9c with such a narrow beam like that of laser communications.

Presumably, the angular speed would be relatively (heh) low if they're moving away from us toward Proxima Centauri.

 

[Umbran]

Well, I was thinking of how hard it would be to hit a small target moving at .9c with such a narrow beam like that of laser communications.

At that distance, a planet is a small target too. Use radio - chew more power, but you're more sure it can be received.

 

[Scott DeWar]

Hrm. There might be a need for some sort of relay system then. That much power even for microwave would need to be immense, on the order of tropospheric scatter level.

 

[Umbran]

Hrm. There might be a need for some sort of relay system then. That much power even for microwave would need to be immense, on the order of tropospheric scatter level.

We already have radio transmitters that we could hear 4 light years away.

 

[Scott DeWar]

And how do we know this? How is this possible?

 

[Umbran]

And how do we know this? How is this possible?

How do we know this? Signal strength drops very predictably with distance. We know the distance, and can calculate the signal strength, and compare that to what signal strengths we already know we can detect.

How is it possible? We have *really good* receivers.

 

[Scott DeWar]

I guess we can extrapolate the effects of 1 billion miles to the ship that just passed Pluto, huh?

I have a different thought forming in my mind, but I need to dwell on the thought a lot more yet.

 

[Umbran]

I guess we can extrapolate the effects of 1 billion miles to the ship that just passed Pluto, huh?

Don't even have to do that. Radio is just light. It follows an inverse-square law - the energy received at some distance D from the source drops off as 1/D^2.

 

[tomBitonti]

For those looking for a (somewhat math-y) summary, I found this:

http://www.ece.rutgers.edu/~orfanidi/ewa/ch16.pdf

Thx!

TomB

 

[tomBitonti]

Something neat that I just found: For lasers and other beam type emitters, there is a thing called the "far field", and (speaking very coarsely), emission does not follow the least square law until the far field is reached.

See, for example:

"The intensity (W/m^2) of an electromagnetic wave from an ordinary antenna decreases with the square of the distance from the emitter (in the far field.) Is the same true for a laser beam?"

https://www.physicsforums.com/threads/do-lasers-suffer-r-2-propagation-loss.473549/

Not just isotropic sources, but any finite source will follow the inverse square law, including lasers. The intensity of the beam is inversely proportional to the square of the beam width. The beam width is proportional to the distance along the beam's axis. So it still works out to be inverse square. However, the beam width also has a constant term and it scales the distance along the axis by another reference value. So it takes an appreciable distance until the beam width behaves asymptotically as proportional to the distance.

Bold added by me.

Then:

In general, the size of a single radiator of an antenna is on the order of a wavelength for efficiency purposes. But we can construct an array of antennas built out of such components that the overall size of the antenna is many wavelengths. The advantage being that an array allows us control over the beam width and angle. Just look at the Very Large Array. Wikipedia gives dimensions of 21 km and a wavelength of 7 mm. That means that the far field of the VLA is around 10^{11} km. That's only 842 Au so that's perfectly suitable for deep space observation. We can also note that the size of the dish is much much larger than the wavelength which is practical because the physics of a dish antenna is different from that of a wire antenna.

Thx!
TomB