Let us assume that sun radiates like a black body with surface temperature at `T_0=6000K` and earth absorbs radiation coming from sun only. If both earth and sun are considered perfect spheres with distance between centre of earth and centre of sun to be 200 times the radius of sun, find the temperature (in Kelvin) of surface of earth in steady state (assume radiation incident on earth to be almost parallel).

Explanation

To solve the problem, we need to find the temperature of the Earth's surface in steady state, given that the Earth absorbs radiation from the Sun, which behaves like a black body.

### Step-by-Step Solution:

1. **Understand the Given Data:**
- Temperature of the Sun, \( T_s = 6000 \, K \)
- Distance between the center of the Earth and the center of the Sun, \( d = 200 \times R_s \) (where \( R_s \) is the radius of the Sun)
- Both the Sun and Earth are considered perfect spheres.
...