What is the acceleration of the Moon as it moves in its circular orbit around Ea

Question

What is the acceleration of the Moon as it moves in its circular orbit around Earth? Hint: You will find some m/s2

     NAME MEAN
ORBITAL
RADIUS
(1011 m) ORBITAL
PERIOD
(years) RADIUS
(106 m) MASS
(1024 kg) ORBITAL
ECCENTRICITY      Mercury      0.579      0.240      2.44      0.330      0.21 Venus 1.08 0.615 6.05 4.87 0.007 Earth 1.50 1.00 6.37 5.98 0.017 Mars 2.28 1.88 3.39 0.644 0.093 Jupiter 7.78 11.9 71.5 1900 0.048 Saturn 14.3 29.4 60.3 568 0.054 Uranus 28.7 83.8 25.6 86.6 0.047 Neptune 45.0 164 24.8 102 0.009 Pluto 59.1 248 1.14 0.125 0.25 Eris 100 560 2.4 — 0.44 Earth's Moon 3.85 108 m 27.3 days 1.74 0.0735 0.055 Sun — — 6.96 108 1.99 1030 —

Explanation / Answer

rbital radius of moon, r = 3.85*10^8 m

orbital time periode of moon, t = 27.3 days

= 27.3*24*60*60

= 2.3587*10^6 m

orbital speed, v = 2*pi*r/T

= 2*pi*3.85*10^8/(2.3587*10^6)

= 1025.6 m//s

radial acceleration of moon towards the Earth, a_rad = v^2/r

= 1025.6^2/(3.85*10^8)

= 2.73*10^-3 m/s^2 <<<<<<<<<--------Answer

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