57. Solar Power Collectors. This problem leads you through thecalculation and discussion of how much solar power can inprinciple be collected by solar cells on Earth.a. Imagine a giant sphere with a radius of 1 AU surroundingthe Sun. What is the surface area of this sphere, in squaremeters? (Hint: The formula for the surface area of asphere is 4rr2.)b. Because this imaginary giant sphere surrounds the Sun,the Sun's entire luminosity of 3.8 × 1020 watts must passthrough it. Calculate the power passing through eachsquare meter of this imaginary sphere in watts per squaremeter. Explain why this number represents the maximumpower per square meter that a solar collector in Earthorbit can collect.c. List several reasons why the average power per squaremeter collected by a solar collector on the ground willalways be less than what you found in part b.d. Suppose you want to put a solar collector on your roof. Ifyou want to optimize the amount of power you cancollect, how should you orient the collector? (Hint: Theoptimal orientation depends on both your latitude andthe time of year and day.)

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. Imagine a giant sphere with a radius of 1 AU surrounding the Sun. What is the surface area of this sphere, in square meters? (Hint: The formula for the surface area of a sphere is 4nr².)