need help solving problem ?

[ritwik]

question is on the page below ↓

http://imagine.gsfc.nasa.gov/YBA/HTCas- ... ength.html

step by step procedure will be very helpful

[Chris Peterson]

question is on the page below ↓

http://imagine.gsfc.nasa.gov/YBA/HTCas- ... ength.html :?:

step by step procedure will be very helpful.

I'd calculate the photon density at 140 pc, 1e32 photons / 2.34e38 m^2 = 4e-7 photons/m^2

and multiply that by the collection area of Arecibo, 7854 m^2, to yield a return signal of 0.003 photons for a single 1e32 photon isotropic pulse.

The site doesn't like that answer, so either the site is wrong, or I'm misunderstanding the question (for instance, why do they specify the frequency?) This appears to be a question in the middle of a sequence of related questions; I didn't look at the others, so maybe I'm missing some different interpretation.

[Markus Schwarz]

Distance to HTcas: R = 140*3.09*10^16 m = 4.33*10^18 m
Number of emitted photons: N = 10^32
Number of photons per square meter = N /(4*pi*R^2) = 4.25*10^-7
Arecibo's collecting area: A = 7854 m^2
Number of photons on Arecibo's collecting area: n = A*N /(4*pi*R^2) = 0.003
Rounding to nearest whole number gives 0

[Markus Schwarz]

[...] return signal of 0.003 photons for a single 1e32 photon isotropic pulse.
The site doesn't like that answer, so either the site is wrong, or I'm misunderstanding the question

I made the same mistake at first. They require you to round to the nearest whole number, which is 0 in this case. Still, I would prefer that they accept 0.003 as well.

[Chris Peterson]

[...] return signal of 0.003 photons for a single 1e32 photon isotropic pulse.
The site doesn't like that answer, so either the site is wrong, or I'm misunderstanding the question

I made the same mistake at first. They require you to round to the nearest whole number, which is 0 in this case. Still, I would prefer that they accept 0.003 as well.

Ha. Borderline trick question. Funny thing is that I tried a couple of alternatives based on possible errors- using one parsec, forgetting to square the radius, and got larger numbers... which I did round to the nearest whole number.

The problem with rounding a very small fractional value to zero is that it actually gives a completely wrong answer. If you genuinely took zero to be the answer here, the conclusion would be that there is no point in sending the probe at all. 0.003 tells us we need a more intense pulse, or more pulses. Rounding up to one would be better than rounding to zero.

[ritwik]

thanks !!

i have trouble with exponents