91Ó°ÊÓ

Mass of ship and sail, m=1500kg .

Sail is perfectly reflected.

Here, we need to use the concept of force developed due to the radiation pressure. The force acting on a perfectly reflective surface of the area as a result of incident radiation of intensity I is given by$\mathbf{F}\backslash \mathrm{user}1=2\mathbf{IAc}$, where$\mathbf{c}$is the speed of light.

Formulae are as follows:

For purely reflecting surface, the radiation pressure, $p=\frac{2I}{c}$.

Where c is the speed of light, and I is the intensity of radiation.

Attractive force due to Sun on mass m is,$F=\frac{Gm{M}_s}{d^2}$

Where M_S is the mass of the sun, F is the force, d is the distance.

The spaceship is propelled in the solar system by the radiation pressure, and at the same time, it’s attracted by the sun. So write force equations as follows:

$F_s=\frac{Gm{M}_s}{d^2}=pA=f_r$

Where A is the surface area of the sail, and p is the radiation pressure, and where F_s, F_r are forces due to sun and radiation.

For purely reflecting surface, radiation pressure,$p=\frac{2I}{c}$

$\frac{Gm{M}_s}{d^2}=\frac{2IA}{c}$

Hence, the Surface area can be calculated as,

$A=\frac{Gm{M}_s}{d^2}×\frac{c}{2I}$

Substitute the values in the above expression, and we get,

$$\begin{gathered} A=\frac{6.67×{10}^{-11}×1500×1.99×{10}^{30}×3×{10}^8}{{\left(1.50×{10}^{11}\right)}^2×2×1.40×{10}^3} \\ =\frac{6.67×15×1.99×3×{10}^{29}}{1.50×2×1.40×{10}^{25}} \\ A=9.5×{10}^5{\text{m}}^{\text{2}} \end{gathered}$$

Therefore, the surface area of the sail, 9.5x10⁵ m² .