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Outline. Universal Gravity. Newton’s Law of Universal Gravitation Course evaluations. On Earth: F g = 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.

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Outline

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  1. Outline Universal Gravity • Newton’s Law of Universal Gravitation • Course evaluations

  2. 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

  3. 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

  4. 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 = 6370kmSmall 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 ???

  5. The force of gravity is: F=GMm/r2and we also know that: F=maIf we equate these two we get: ma=GMm/r2 a =GM/r2Subbing in G, M (earth) and r (radius of earth) we get: a=9.8m/s2

  6. 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 h r

  7. 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/s21.6/9.8 = 1/6, therefore, you would weight about 1/6 as much on the moon as you do on earth !

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