The Luminosity of a Star

How Much Light Does a Star Emit

The luminosity of a star represents the total output of radiant energy per second. We can grasp this quantity most easily by thinking of the luminosity of the star in comparison with that of our sun. A star 100 times as luminous as the sun, would emit 100 times as much radiant energy per second as our sun does.

Replacing the Sun

What would be the effect of replacing our own star, the sun, with another star of different luminosity?

The Effective Temperature of a Planet

The temperature of a planet like the earth is the result of a balance between the energy received from the sun, and energy radiated back into space. With the assumption that all of the energy received from the sun is absorbed by the earth, the effective temperature of the earth turns out to be out 278 K, that is, about 5 °C. This value is a reasonable first approximation to the actual average surface temperature of the earth, given the luminosity of the sun.

Global Warming with a Vengeance

The effective temperature of the earth scales as the fourth root of the luminosity of the sun. If we were to replace the sun with a star 10 times as luminous as the sun, the effective temperature on the earth would increase as the fourth root of 10, that is, 1.78. So the effective temperature on our planet would become 494 K, that is, about 220° C.

This temperature increase is far higher than anything that would be produced by the global warming projected for the next century. Replacing the sun by the more luminous star would produce temperatures on earth far above the boiling point of water. It is safe to say that with such a star in place of the sun, there would be no life on earth.

Moving to Cooler Regions

Another way of looking at the temperature problem is to look at the distance from the star. How far from the star would the earth have to be to maintain the temperature that we have now?

The principle is that the further a planet is from the star, the cooler the temperatures will be. The distance scales with the square root of the luminosity, assuming that the effective temperature is to remain the same.

So if we were to replace the sun by a star 10 times as luminous, the earth would have to increase the radius of its orbit by the square root of 10, that is, 3.16, if we were to enjoy the same temperatures that we enjoy today. This would correspond to an orbit in the middle of the asteroid belt between the orbits of the planets Mars and Jupiter.

A Problem for the Reader

What would the effective temperature of the earth be, if the sun were replaced by a star 10,000 times as luminous as the sun?

Where would the earth have to orbit to have today's temperatures, if the sun were replaced by a star 10,000 times as luminous?

Here are the answers.  

 


Copyright © 1998 - 2010 by Arnold V. Lesikar,
Professor Emeritus
Dept. of Physics, Astronomy, and Engineering Science,
St. Cloud State University,St. Cloud, MN 56301-4498

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