**Problem 1: Sun's Mass Loss Due to Nuclear Reactions and Solar Wind****a)** Calculate the rate at which the Sun's mass is decreasing due to nuclear reactions (\(\Delta m/\Delta t\)). Use the formula \(E=mc^2\) and the given solar luminosity (\(L_{\text{Sun}} = 3.839 \times 10^{26}\) W). Provide your answer in solar masses per year (\(M_{\text{sun}}/\text{year}\)).**b)** Determine the rate of mass loss due to solar wind. Use the given parameters: velocity \(v = 500\) km/s (as measured on Earth), particle density \(n = 7 \times 10^6\) particles/m\(^3\), and mean molecular weight \(\mu = 1\).**c)** Assuming that the rates from both processes remain constant throughout the Sun's main-sequence lifetime (approximately \(10^{10}\) years), evaluate whether either mass loss process would significantly affect the Sun's total mass.

Answered: Image /qna-images/answer/296c0f76-532e-46e6-a9aa-3d2ac6eb0127.jpg

1) a) At what rate is the Sun's mass decreasing due to nuclear reactions Am/At? Use E=mc² and Lsun=3.839x1026 W and give your answer in Msun/year. b) And due to solar wind? Calculate the flow using v=500 km/s measured on Earth, n=7x106 particles/m³ and u=1. c) Assuming that those 2 processes rates remain constant during the Sun's main-sequence life, would either mass loss process significantly affect the total mass of the Sun? Use that the Sun's lifetime in the main-sequence is ~ 1010 years.

1) a) At what rate is the Sun's mass decreasing due to nuclear reactions Am/At? Use E=mc² and Lsun=3.839x1026 W and give your answer in Msun/year. b) And due to solar wind? Calculate the flow using v=500 km/s measured on Earth, n=7x106 particles/m³ and u=1. c) Assuming that those 2 processes rates remain constant during the Sun's main-sequence life, would either mass loss process significantly affect the total mass of the Sun? Use that the Sun's lifetime in the main-sequence is ~ 1010 years.