Problem 2 Internal Temperature of the Sun versus a Brown Dwarf The Sun is essentially a gas cloud in which the forces of pressure and gravity balance each other. We can therefore use the equation in Mathematical Insight 16.1 to estimate the interior temperature of the Sun from its mass and particle density. Problem 2.1 10 pt: - What is the average number density of particles within the Sun, given that the average mass per particle is about 10 '24 gram '2 (Hint : The volume of a sphere of radius r is equal to 4r3/3.) Problem 2.2 10 pts What is the approximate temperature necessary for gas pressure to balance gravity within the Sun , given the average particle density from Part 1.1'? How does your estimate compare with the internal core temperature of the Sun ? Problem 2.3 10 pts - The maximum temperature inside a brown dwarf is the temperature at which thermal pressure would balance gravity. In reality, degeneracy pressure halts the contraction of a brown dwarf before it can reach that maximum value. You can use the formula in Mathematical Insight 16.] to estimate the maximum interior temperature of a brown dwarf with a mass of 0.05 M m and a radius of 0.] Rm. What is the average number density of particles inside the brown dwarf, given that the average mass per particle is about 10'\" gram