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 correct answer is option (c) 9

Step-by-step 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

Answer 2

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}} = (r_1^2)/(r_2^2)`

`(P_1)/(P_2) = ((18)/(6))^2`

`(P_1)/(P_2) = 9`

Therefore the correct option is option C.9