Complete Question
A large solar panel on a spacecraft in Earth orbit produces 1.6kW of power when the panel is turned toward the sun.
What power would the solar cell produce if the spacecraft were in orbit around Saturn, 9.5 times as far from the sun?
Answer:
The power is [tex]P_2 = 17.73 \ W[/tex]
Explanation:
From question we are told that
The power produced by the spacecraft is [tex]P_1 = 1.6 kW = 1.6 *10^{3} \ W[/tex]
The distance of the earth orbit from the sun is R
The distance of the Saturn's orbit from the sun is 9.5 R
Generally the power produced by a solar panel is mathematically represented as
=> [tex]P \ \alpha \ \frac{1}{R^2}[/tex]
[tex]P = \frac{k}{R^2}[/tex]
Here k is a constant
So
[tex]P_1 = \frac{k}{R^2 }[/tex]
=> [tex]k = P_1 * R^2[/tex]
while
[tex]P_2 = \frac{k}{[9.5R]^2 }[/tex]
Here [tex]P_2[/tex] is the power produce by the solar panel when at Saturn's orbit
=> [tex]k = 90.25 R^2 * P_2[/tex]
So
[tex]P_1 * R^2 = 90.25 R^2 * P_2[/tex]
=> [tex]P_2 = \frac{1.60 *10^3}{90.25}[/tex]
=> [tex]P_2 = 17.73 \ W[/tex]
