An astronomer on a planet orbiting the star Deneb wants to d

An astronomer on a planet orbiting the star Deneb wants to differentiate the reflected light by Earth from the light of the Sun. First, consider a spherical shell with the same radius as Earth’s orbit around the Sun through which all the Sun\'s light passes through. Second, consider the area of Earth\'s disk at the distance of the spherical shell which reflects the Sun\'s intercepted light. Take the ratio of these two considerations. Assume the Earth\'s radius is 6400.0 km and is 1.3 × 10^8 km from the Sun. Recall the surface area of a sphere is 4 rsphere^2 and the surface area is a disk is rdisk^2.

Solution

power output of sun, P = 3.846 x 10^26 W

distance from sun, r = 1.3 x 10^11 m

intensity reaching earth surface,

I = P / (4 pi r^2) = 1811 W/m^2

Energy at surface of earth = I ( pi R^2)

= (1811) ( pi (6400 x 10^3)^2)

= 2.33 x 10^17 W