The effective temperature of a planet is the temperature it would have if
it acted like a black body, absorbing all the incoming radiation received
at its surface and reradiating it all back to space.
With the following facts you can easily calculate the effective
temperature of the Earth and, if you know the distance to the other planets,
their effective temperatures as well.
Distance from Earth to Sun = 150x106
Radius of the Sun = 6.96x108 meters.
Radius of the Earth = 6.4x106 meters.
Surface area of a sphere = 4pr2.
Area of a circle = pr2.
p = 3.1416.
Maximum output from the Sun occurs at a wavelength of 0.5 microns.
Lets walk through the steps together:
The Earth intercepts a small part of the total radiation that arrives in its neighborhood of the solar system (its distance from the Sun). If we could hold an enormous sheet of paper on the other side of the Earth from the Sun and orient it so the plane of the paper is perpendicular to the rays of the Sun, then the earth would cast a shadow on the paper and the area of that shadow would be the amount of solar radiation the Earth intercepts. This circular shadow will have a radius equal to the radius of the Earth. If you calculate the area of the shadow and multiply it by the intensity of the solar beam at the Earth's distance from the sun, you will have the total energy the Earth intercepts. Now the Earth rotates like a chicken on a rotisserie and is heated on all sides. Therefore, the area that receives the radiant energy from the Sun is not that of a disk, like the shadow of the Earth on the paper, but that of a sphere which has a different surface area. Calculate the average radiation (Watts/square meter) the Earth's surface receives from the Sun.