Calculation of Equilibrium Temperature

Given parameters:

- Absorptivity of the space vehicle surface = 0.4
- Emissivity of the space vehicle surface = 0.6

Step 1: Calculation of Solar Flux Intensity

As the solar flux of intensity directly strikes the space vehicle surface, we need to calculate its intensity first. Let's assume the intensity of solar flux as 'I'.

Step 2: Calculation of Absorbed Solar Flux

The space vehicle surface absorbs a fraction of the incident solar flux, which is equal to its absorptivity. Hence, the absorbed solar flux is given by:

Absorbed Solar Flux = Absorptivity x Solar Flux Intensity
= 0.4 x I

Step 3: Calculation of Radiative Heat Transfer

The space vehicle surface also radiates heat due to its emissivity. The radiative heat transfer from the surface is given by:

Radiative Heat Transfer = Emissivity x Stefan-Boltzmann Constant x (Equilibrium Temperature)^4
= 0.6 x 5.67 x 10^-8 x (Equilibrium Temperature)^4

Step 4: Calculation of Equilibrium Temperature

At equilibrium, the absorbed solar flux is equal to the radiative heat transfer. Hence, we can equate the expressions obtained in Step 2 and Step 3 and solve for the equilibrium temperature:

0.4 x I = 0.6 x 5.67 x 10^-8 x (Equilibrium Temperature)^4

Equilibrium Temperature = (0.4 x I / (0.6 x 5.67 x 10^-8))^0.25

Step 5: Calculation of Equilibrium Temperature for I = 1366 W/m2

The solar constant, which is the average solar flux intensity at the Earth's distance from the Sun, is approximately 1366 W/m2. Hence, we can substitute this value for 'I' in the expression obtained in Step 4 and solve for the equilibrium temperature:

Equilibrium Temperature = (0.4 x 1366 / (0.6 x 5.67 x 10^-8))^0.25
= 300 K

Therefore, the equilibrium temperature of the space vehicle surface in space at 0 K is 300 K (option A).