MadSci Network: Astronomy

Re: How do we see stars if light is emitted in a spherical pattern?

Date: Mon Dec 5 22:31:39 2005
Posted By: Bryan Dunne, Grad student, Astronomy, University of Illinois
Area of science: Astronomy
ID: 1133785496.As

It comes down to sheer numbers. Let's start off with something a little more familiar---a 100-Watt light bulb. A Watt is a measurement of the rate of flow of energy. One Watt is 1 Joule per second. (For reference, there are about 4000 Joules of energy in every Calorie of food you eat.) Therefore, our light bulb generates 100 Joules of light per second, but the typical energy of a photon from our light bulb is about 0.0000000000000000004 Joules. That means that our light bulb emits about 250,000,000,000,000,000,000 (250 quintillion) photons per second!

[The energy of a photon is given by hc/lambda, where h = 6.63 x 10-34 m2 kg/s is Planck's constant, c = 3 x 108 m/s is the speed of light, and lambda is the wavelength of the light. Our eyes see light with wavelengths of about 500 nm, or 5 x 10-7 m. Moderator]

Now, let's scale up to our Sun, a fairly average star. Our Sun emits 400,000,000,000,000,000,000,000,000 (400 septillion) Joules per second, or 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 (1 quattuordecillion----that's a 1 followed by 45 zeroes) photons per second!

Even at a distance of 10 light years (about 100 trillion kilometers) from our star, there are still about 10,000 photons per square millimeter of the expanding sphere you talked about. Now, the pupil of our eye has a diameter of about 8 millimeters in dim light. That gives a light-collecting area of about 50 square millimeters, or enough area to collect 500,000 photons per second from the star.

[However, this does illustrate why astronomers want large telescopes. Imagine how many photons your eye collects from a distant galaxy. Large telescopes are necessary to collect even a modest number of photons from extremely distant objects. Moderator]

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