Prof. Chaos like to like to place an 80 kg satellite in a geostationary orbit (o

Question

Prof. Chaos like to like to place an 80 kg satellite in a geostationary orbit (orbit maintains the same position relative to Earth's surface). Calculate the altitude necessary to achieve a circular orbit at GEO. The radius of the Earth is 6375 km, and the mass of Earth is about 6 times 10^24 kg. An electron has a mass of about 9.109 times 10^-31 kg and, classically, was assumed to have a radius of about 2.8 times 10^-15 m. Considering the Schwartz child Radius is R_s = 2GM/c^2, where c is the speed light (almostequalto 3 times 10^8 m/s), can an electron be considered a black hole?

Explanation / Answer

for GEO time period T = 24 hours = 24*60*60 s = 86400 s

time period T^2 = 4*pi^2*r^3/(GM)

r = R + h

R = radius of earth = 6375000 m

h = altitude

M = mass of earth = 5.97*10^24 kg

86400^2 = 4*pi^2*(6375000+h)^3/(6.67*10^-11*5.97*10^24 )

h = 35852 km

h = 3.6*10^7 m <<<--------answer

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(2)

schwartzchild radius of electron Rs = 2*6.67*10^-11*9.109*10^-31/(3*10^8)^2

Rs = 1.35*10^-57 m

radius of electron r = 2.8*10^-15 m

r > Rs

No electron is not considered as a black hole

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