2. (10) Consider the Sun to be a sphere of uniform density...

2. (10) Consider the Sun to be a sphere of uniform density that derives its luminosity from steady contraction - not from nuclear burning! a. The gravitational potential energy is defined as: $U = \frac{3GM_\odot^2}{5R_\odot}$ , where the factor of 3/5 is a geometric factor (here, we assumed a uniform sphere). Confirm that the units of this equation are in fact units of energy. b. What is the gravitational potential energy (in erg) of the Sun at its current radius? c. In this scenario, we assume that the gravitational energy goes into the Sun's luminosity. In particular: $L = \frac{U}{time}$ If this were true, the radius would shrink over time! Write a symbolic equation for the radius of the Sun T years ago, assuming that the current radius is $R_\odot$. d. How much should the radius have decreased over the last 5000 years (roughly modern times)?

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Consider the Sun to be a sphere of uniform density that derives its luminosity from steady contraction - not from nuclear burning! a. The gravitational potential energy is defined as: U=(3)/(5)(GM_(o.)^(2))/(R_(o.)), where the factor of (3)/(5) is a geometric factor (here, we assumed a uniform sphere). Confirm that the units of this equation are in fact units of energy. b. What is the gravitational potential energy (in erg) of the Sun at its current radius? c. In this scenario, we assume that the gravitational energy goes into the Sun's luminosity. In particular: L=(U)/( time ) If this were true, the radius would shrink over time! Write a symbolic equation for the radius of the Sun T years ago, assuming that the current radius is R_(o.). d. How much should the radius have decreased over the last 5000 years (roughly modern times)? Can you solve c) step by step very clearly? When I checked the book, the gravitational potential energy U equation is actually negative, but what does negative tell us about it? (Please do not waste my question ever again only for your own purpose who just did to my previous one. You could answer to my question and then copy and paste your statement, but you didn't.) 2. (10) Consider the Sun to be a sphere of uniform density that derives its luminosity from steady contraction -- not from nuclear burning! a. The gravitational potential energy is defined as: 3GMo2 U 5 Ro , where the factor of 3/s is a geometric factor (here, we assumed a uniform sphere). Confirm that the units of this equation are in fact units of energy. b. What is the gravitational potential energy (in erg) of the Sun at its current radius? c. In this scenario, we assume that the gravitational energy goes into the Sun's luminosity. In particular: U time If this were true, the radius would shrink over time! Write a symbolic equation for the radius of the Sun T years ago, assuming that the current radius is Ro. d. How much should the radius have decreased over the last 5000 years (roughly modern times)?

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