Universal Gravity Newton’s Law of Universal Gravitation

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Presentation transcript:

Universal Gravity Newton’s Law of Universal Gravitation Course evaluations Outline

On Earth: Fg = mg, where m is the mass of an object and g is the acceleration due to gravity. This equation is valid only near the surface of the earth ! m Earth

Anywhere else, Fg = GMm/r2, where M and m are the masses, r is their separation and G is the universal gravitational constant. M m r

We can use F=GMm/r2 on the surface of the earth, but the equation is more complicated. We need to: - use G=6.67x10-11 Nm2/kg2 - use the mass of the earth, M=5.98x1024kg - and know the distance of the object from the center of the earth, Re = 6370km Small differences in r (eg, 10, 100 or 1000m) will not make a large difference in the force. So, how do we get to F=mg ???

The force of gravity is: F=GMm/r2 and we also know that: F=ma If we equate these two we get: ma=GMm/r2 a =GM/r2 Subbing in G, M (earth) and r (radius of earth) we get: a=9.8m/s2

Because F=GMm/r2, we can see that F will decrease with r. Also, since g=GM/r2, g will decrease with r as well: at h=100km g=9.5m/s2 at h=1000km g=7.3m/s2 r h

Eg: The mass of the moon is M=7.36x1022 kg, its radius is r=1.74x106m. What is the value of g on the moon? (6.67x10-11Nm2/kg2)(7.36x1022 kg) g=GM/r2 = ___________________________ (1.74x106 m)2 = 1.6 m/s2 1.6/9.8 = 1/6, therefore, you would weight about 1/6 as much on the moon as you do on earth !