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Chapter 15: Problem 75

A satellite in a circular orbit around the Sun uses a square solar panel as a power source. The panel's efficiency is \(16.87 \% .\) The satellite is \(6.103 \cdot 10^{7} \mathrm{~km}\) from the Sun. The solar panel provides \(5.215 \cdot 10^{3} \mathrm{~W}\) to the satellite. How long are the edges of the solar panel? Assume that the total power output of the Sun is \(3.937 \cdot 10^{26} \mathrm{~W}\).

Short Answer

Expert verified
Answer: The length of each edge of the satellite's solar panel is approximately \(0.4819\) meters.

Step by step solution

01

Convert Distance to Meters

The distance of the satellite from the Sun is given in kilometers, so we need to convert it to meters. \((6.103 \cdot 10^{7} km)\times (1,000 m/km) = 6.103 \cdot 10^{10} m\)
02

Calculate Solar Intensity at Satellite

Next we need to calculate the intensity of sunlight at the satellite. We use the energy output of the Sun and the satellite's distance from the Sun to calculate the intensity: \(Intensity = \frac{Energy~Output}{4 \pi (Distance)^2}\) \(Intensity = \frac{3.937 \cdot 10^{26} W}{4 \pi (6.103 \cdot10^{10} m )^2}\) \(= \frac{3.937 \cdot 10^{26} W}{4 \pi (3.727 \cdot 10^{21} m^2)}\) \(Intensity = 1.33 \cdot 10^{5}~W/m^2\)
03

Determine the Absorbed Solar Power

Now we need to calculate the actual solar power that the panel absorbs, taking into account its efficiency. To do this, we simply multiply the intensity by the panel's efficiency. \(Absorbed~Power = Intensity \times Panel~Efficiency\) \(Absorbed~Power = (1.33 \cdot 10^{5} W/m^2)(0.1687)\) \(Absorbed~Power = 2.242 \cdot 10^{4} W/m^2\)
04

Determine the Area of the Panel

Since we know the power provided by the panel to the satellite, we can find the area by dividing the provided power by the absorbed power per square meter: \(Panel~Area = \frac{Provided~Power}{Absorbed~Power} = \frac{5.215 \cdot 10^3 W}{2.242 \cdot 10^4 W/m^2}\) \(= 0.2323 m^2 \)
05

Calculate the Length of the Panel's Sides

Lastly, we need to determine the length of each edge of the square solar panel. Since the area of a square is equal to the side length squared, we can find the side length by taking the square root of the area: \(Side~Length = \sqrt{Panel~Area} = \sqrt{0.2323 m^2} = 0.4819 m\) The length of each edge of the satellite's solar panel is approximately \(0.4819\) meters.

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Most popular questions from this chapter

A small ball floats in the center of a circular pool that has a radius of \(5.00 \mathrm{~m}\). Three wave generators are placed at the edge of the pool, separated by \(120 .^{\circ}\). The first wave generator operates at a frequency of \(2.00 \mathrm{~Hz}\). The second wave generator operates at a frequency of \(3.00 \mathrm{~Hz}\). The third wave generator operates at a frequency of \(4.00 \mathrm{~Hz}\). If the speed of each water wave is \(5.00 \mathrm{~m} / \mathrm{s}\), and the amplitude of the waves is the same, sketch the height of the ball as a function of time from \(t=0\) to \(t=2.00 \mathrm{~s}\), assuming that the water surface is at zero height. Assume that all the wave generators impart a phase shift of zero. How would your answer change if one of the wave generators was moved to a different location at the edge of the pool?

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