Inverse Square Law
Newton's
law of gravity
describes a force that decreases with the SQUARE of the distance. For
every factor of 2 the distance increases, the gravitational attraction
decreases
by a factor of 2 × 2
= 4; for every factor of 3 increase in distance, the gravity decreases by a factor of 3 × 3 = 9 (not
by 3 + 3 = 6!); for every factor of 4 increase in distance, the gravity decreases by a factor of 4 ×
4 = 16 (not by 4 + 4 = 8!), etc. See the
mathematics review appendix
for a review of ``factor'' and
``times''. Some more examples are given in the table below. Notice how quickly an inverse
square law gets very small.
A comparison of inverse and inverse square relations
distance
inverse
inverse square
1
1/1 = 1
1/1
2
= 1
2
1/2 = 0.5
1/2
2
= 1/4 = 0.25
3
1/3 = 0.33
1/3
2
= 1/9 = 0.11
4
1/4 = 0.25
1/4
2
= 1/16 = 0.0625
7
1/7 = 0.14
1/7
2
= 1/49 = 0.02
10
1/10 = 0.1
1/10
2
= 1/100 = 0.01
100
1/100 = 0.01
1/100
2
= 1/10,000 = 0.0001
Example: Joe Average has a mass of 63.5 kilograms, so he weighs 623 newtons (=140 pounds)
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 Fall '10
 EmilyHoward
 Astronomy, Mass, General Relativity, inverse square, Joe Average

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