Constants, conversion factors and some formulas: k = 8.988 . 10^9 N.m^2/C^2 epsi

Question

Constants, conversion factors and some formulas: k = 8.988 . 10^9 N.m^2/C^2 epsilon0 = 8.854 . 10^-12 C^2/N.m^2 Mu0 - 4pi . 10^-7 T.m/A e = 1.602 . 10^-19 C c = 3.00 . 10^8 m/s G = 6.67 . 10^-11 N.m^2/kg^2 pico (p) nano (n) micro (Mu) milli (m) centi (c) kilo (k) mega (M) giga (G) 10^-12 10^-9 10^-6 10^-3 10^-2 10^3 10^6 10^9 Centripetal acceleration aCP = v^2/R 9. The Moon rotates around the Earth on a nearly circular orbit with an average radius of Rorbit = 3.85 x 10^8 m. The mass of the Earth (ME) is 5.98 x 10^24 kg, and the mass of the Moon (MM) is 7.35 x 10^22 kg. (a) Calculate the force of gravitational attraction between the Moon and the Earth. (b) Calculate the centripetal acceleration of the Moon in orbit. (c) Calculate the tangential speed of the Moon in orbit. Extra Credit: calculate the period of rotation of the Moon around the Earth, express the result in seconds and in days. What is the significance of this time interval (is it known by any other name?) Circumference of a circle = 2piR

Explanation / Answer

a) F = G M m/r^2 = 6.67E-11*5.98E24*7.35E22/3.85E8^2= 1.98E20 N

b) amoon = F/mmoon = G Merath/r^2= 6.67E-11*5.98E24/3.85E8^2= 2.69E-3 m/s^2

c) a = v^2/r

v = sqrt( a r) = sqrt(2.69E-3*3.85E8)= 1018 m/s

extra credit

v = 2 pi R/T

T = 2 pi r/v = 2*pi*3.85E8/1018= 2.38E6 s = 27.5 days

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