The sun uses fusion to produce the energy it radiates into space. This energy co
ID: 2259199 • Letter: T
Question
The sun uses fusion to produce the energy it radiates into space. This energy comes from a loss of mass (i.e. mass is being converted into energy and the sun is losing mass in the process). The radius of the Earth's orbit is 1.5 * 10^8 km and the intensity of solar radiation at Earth (solar constant) is 1.36 * 10^3 W/m^2.
A) Compute the rate at which the sun is losing mass (in kg/second). Use Einstein's mass-energy equivalence equation, E=mc^2 for your calculation (note: c = speed of light = 3 * 10^8 m/s). HINT: the solar constant at Earth is the amount of energy the sun radiates in all directions through an imaginary sphere with the same radius as the Earth's orbit.
B) What is the solar constant at Jupiter (mean orbital radius = 8.0 * 10^8 km)?
Explanation / Answer
A) The total surface area of imaginary sphere of radious of earth's orbit A = 4 pi R^2<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />
A= 4*(22/7)*(1.5*10^11)=18.86*10^11 m^2
Power = Energy per second = (solar constant)*(Area)=1.36*10^3*18.86*10^11
= 25.64*10^14 W or J/s
From E=mc^2, mass per second= (Energy per second)/c^2
= (25.64*10^14)/(9*10^16)
= 2.85*10^-2
= 28.5 gm per second
B) The total surface area of imaginary sphere of radious of jupiter's orbit A = 4 pi R^2
A= 4*(22/7)*(8*10^11)=100.6*10^11 m^2
From E=mc^2, Energy per second = (mass per second)c^2
= 2.85*10^-2*9*10^16
= 25.64 * 10^14 Watt
Solar constant of Jupiter = P/A=25.64* 10^14/100.6*10^11
= 0.2549*10^3 W/m^2
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