Thursday, August 06, 2009

The Pacific Ocean is 2.5 trillion km wide

According to Cosmic Variance, the Bones episode on which Sean consulted was transmitted at 8 pm on 9 April 2009. On 12 July 2009 this broadcast was received here in Australia, where I watched the show.

Because TV transmissions are electromagnetic radiation, and travel at the speed of light, we can use this delay to determine the distance between California and Australia. The delay was 94 days, which is 0.26 years. So the distance is 0.257 light years. This is about 2.4 trillion kilometers, or 16,000 astronomical units. Thus the width of the Pacific Ocean (which separates California and Australia) is slightly larger than the distance between Proxima and Alpha Centauri, in the closest stellar system to our own.

Now, some of you may find this hard to believe. After all, surely if you can’t clearly get channel 6, then a TV transmission from 2 and a half trillion km would be hopeless, right?

Not necessarily.

Here in Canberra, our NASA Deep Space Network is currently tracking Voyager 1 at a distance of 110 au. This is 147 times closer than California. Assuming that radio transmission strength follows an inverse squared distance law, the signal from a California radio station broadcasting from the edge of interstellar space would be 22 thousand times weaker than that from Voyager 1 for a given transmitter power.

Luckily, that power is not constant. Voyager 1 has a 20 watt X-band transmitter. In contrast, San Francisco’s KCNS (UHF channel 38) pumps out an effective radiated power of 5000 kilowatts; 250,000 times more power. As a result, even at the astronomical distance at which California lies, the TV stations there still have up to ten times more signal than the old space probe.

Thus, my interpretation of California being on the outer edge of the Oort Cloud is entirely plausible.

The take home message, of course, is that when people accuse Californians of being way out there, they are vastly understating the situation…

2 comments:

Jazinator said...

So does that mean that plane tickets are invariable cheep then?

Assuming the distance and all.

Legolas Greenleaf said...

Lol. Your theory of CA being on the edge of the "Oort Cloud" is entirely plausible! Haha.