Distance from a star to receive the same heat as Earth?

Question

I was wondering if anyone has ever come up with a formula to calculate the distance, and revolutions in "earth years", a planet would have to be from any given star given the radiation output of the star, the diameter of the star and giving the hypothetical planet the same mass and density of the Earth.

Answer 1

If you know the star's luminosity, you can do this....

Lum = Star's Luminosity (relative to the sun), AU = distance from the star in Astronomical Units (relative to earth distance), IR = Incident Radiation (earth from sun Relative)

Lum/ AU^2 = IR

Then it gets a little more complicated.

(IR * (Albedo / Earth Albedo))^.25

Basically this formula takes the IR and applies it to one half of the planet and factors in Albedo (reflectivity)

The number that you get is a rough temperature relative to what the earth would be without an atmosphere...

Take the number and multiply by about 288, (this gives you a rough estimate of the temperature of the planet in Kelvins, if the planet has the same atmospheric composition as Earth). To find out more, the math gets more complicated-- you have to factor in atmospheric mass, density, pressure, and composition--including some things to make certain to account for the greenhouse effect, etc.

Hope this gets you started in the right direction!

Answer 2

Yes, they have. The range of space around a star where a planet could support liquid water is called the "Goldilocks" zone (by some) or the "green" zone by others.
Within that zone there will be a precise distance from the star where the planet would receive the same amount of heat as the earth does (on average) from our sun.
It depends on the star's surface temperature and size.

Answer 3

The easy way:

For revolution, use Newton's modification of Kepler's Third Law:

MP^2 = A^3

where:
M = mass of the star (or combined masses, if you want to be more specific)
P = orbital period in years
A = distance in AUs

For illumination, just take the square root of the brightness of the star relative to the Sun to get the relative distance. For instance, if a star is twice as bright as the Sun, the "safe" distance will be the square root of two in AUs, or 1.4 AUs.

Of course, this is a simplification: it doesn't take into account the different amounts of radiation stars of varying radiation give off (hot stars give off more UV, and cool stars more IR), among other things.

Answer 4

If the star is four times as bright as the Sun, the planet would have to be twice as far away. It is simply an inverse square relationship. The size of the star or planet does not matter at all.

Answer 5

Do you mean minimum distance and still be able to support life? This is already calculable. It think it's called the "green zone" of habitability around any star.