Question

If the average density of the universe is at least 6.0 x 10"27 kg/m3, then the universe will eventually stop expanding and begin contracting (a) How many electrons are needed in each cubic meter to produce the critical density? (me 9.11 x 10-31 kg) electrons/m (b) How many protons per cubic meter would produce the critical density? (mp 1.67 x1027 kg) protons/m3 eBook -10.62 points Tipler6 1.P075. My Notes Ask Your Teac The table below gives the periods T and orbit radii r for the motions of four satelites orbiting a dense, heavy asteroid. (a) Period T,y (b) Radius r, Gm 0.44 1.61 3.88 7.89 0.088 0.208 0.374 0.600 (a) These data can be fitted by the formula T- C. Find the values of the constants C and n. C- (b) A fifth satellite is discovered to have a period of 8.17 y. Find the radius for the orbit of this satellite, which fits the same formula. Gm

Answer 1

rho = 6 times 10^-27 kg/m^3 1 m^3 contains 6 times 10^-27 kg mass If n electrons are in 1 m^3 volume then n times 9.11 times 10^-31 = 6 times 10^-27 n = 6 times 10^-37/9.11 times 10^-31 = 6586 n = 6586 electrons/m^3 n times 1.67 times 10^-27 = 6 times 10^-27 n = 6 times 10^-27/1.67 times 10^-27 = 3.59 n = 3.59 protons/m^3