Suppose that there is a planet in the solar system with a semi-major axis of a, of 77.2 A.U.that is an icy?

Question

object with an albedo A, of 0.50. What is its surface temperature assuming that its only source of heat is sunlight, and that the planet radiates as a black body. Suppose that th eplanet has the mass and radius of pluto. WOuld such a planet be expected to retain carbod Dioxide ( mass=44xmass of hydrogen)?

Answer 1

This one is a bit challenging! Are you taking a junior (3000 or 300) level astrophysics course?

To find the temperature, assume it spins fast enough to be at equilbrium all over. Figure out the energy input by multiplying

A*L_sun/d^2*pi*r_planet^2

A=albedo, L_sun is the solar luminosity,d is that semi-major axis, and pi*R_planet^2 is the cross sectional area of the planet.

Now you are going to assume that the planet is in equilibrium; namely that the emitted radiation equals the absorbed radiation. So, set that equation equal to the Stefan-Boltzmann equation (I am sure you know where to find this one; it is the one with T^4 in it) and solve for T.

Now, you can do the same calculation you did with the Earth retaining Hydrogen one, or you can look up the physical properties of carbon dioxide and possibly see a short cut. . . . .

Answer 2

Wow, sounds like a waste of time. I know that an astronomical unit is the distance between the sun and earth, so if this planet was 77.2 A.U.'s, it would be extremely cold, especially since its so small. Can it retain carbon dioxide? Who knows. The scientists are only theorizing in their studies.