Friday, January 2, 2009

ACCELERATION DUE TO GRAVITY

g = GM/r^2

where:
g = acceleration due to gravity
G = Newton's gravitational constant 6.67 x 10^-11
M = mass
r = radius


39940.65265km = polar circumference of the earth
40075.01669km = equatorial circumference
5.9742x1024kg = mass of the earth

-21.3847km difference in radius to the center of the earth between equatorial radius of 6378.137km and polar radius of 6356.7523km

1° latitude = 110.946km = -.237608km difference in radius to the center of the earth travelling from the equator to the pole

9.79530367199 m/s^2 = acceleration due to gravity at the equator
9.86131913338 m/s^2 = acceleration due to gravity at the pole

.06601546139 m/s^2 difference between the pole and the equator = 7.335051266x10^-4 m/s^2 per degree latitude

.237608km = -7.335051266x10^-4m/s^2 difference in acceleration due to gravity

1000m in elevation = -3.087x10^-3m/s^2 = -.0315% weight difference
31.7460317km in elevation = 1% weight difference
w = mg

84kg mass at the equator = 822.80550844716 newtons
84kg mass at the pole = 828.35080720392 newtons

828.35080720392/g at the equator = 84.56611810541586kg at the pole (which we mistakenly refer to as weight. mass of course remains the same wherever in the universe you are)

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