Question

Two spacecraft are both 10 million kilometers from a star. The total power output of the star is 4 x 1025 W. Spacecraft 1 has a solar panel with a radius of 18 m. Spacecraft 2 has a solar panel with a radius of 6 m. What is the ratio of the power collected by the solar panel of Spacecraft 1 to the power collected by the solar panel of Spacecraft 2. a. 0.11 b. 0.06 c. 9 d. 18 e. 1 f. 0.33 g. 3

Answer 1

The concept of power is given by the relationship between intensity and area, that is to say that power is defined as

$P = A*I$

Our values are given under the condition of,

$r_1 = 18m$

$r_2 = m$

The power is proportional to the Area, and in turn, we know that the Area of a circle is the product between $\pi$  times the radius squared, therefore the power is proportional to the radius squared.

$\text{Power} \propto r^2$

For both panels we would have to

$\frac{\text{Power by panel 1}}{\text{Power by panel 2}} = \frac{r_1^2}{r_2^2}$

$\frac{P_1}{P_2} = (\frac{18}{6})^2$

$\frac{P_1}{P_2} = 9$

Therefore the correct option is option C.9

Answer 2

Answer:

the correct answer is option (c) 9

Explanation:

solution;

Given data;

radius of spacecraft 1 = 18m

radius of spacecraft 1 = 6m

The total power output of the star = 4 x 1025 W

power is given by the formula;

P = I * A

where I is light intensity and A is the area

but power can be said to be proportional to area.

Since area = πr² therefore, power is proportional to r²

The equation becomes,

power of panel 1 /power of panel 2 = r₁²/r₂²

                                                          = 18²/6²

                                                          = 324/36

                                Ratio                     = 9