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Idea: Newton's Universal Law of Gravitation states that
any two objects
exert a gravitational force of attraction on each
other. The direction of the force is along the line joing the
objects (See Fig.(7.3)). The magnitude of the force is
proportional to the product of the gravitational masses of the
objects,
and inversely proportional to the square of the distance between
them.
For the two objects in Figure 7.3:
= - .
F_{12} = G. | (22) |
G = 6.67 x 10^{- 11} N m ^{2} /kg ^{2}. | (23) |
Note:
F_{grav} = - Gm = - mg | (24) |
g G = 9.8 m/s ^{2} | (25) |
Definition: Gravitional Potential Energy
Due to the gravitational force of attraction, any two objects with masses m_{1} and m_{2} located a distance r apart have the ability to do work. Hence they have potential energy. The gravitational potential energy of such objects is:
PE_{ grav} = - G. | (26) |
Note:
PE_{ grav} = - G.
If h < < R_{E} we can approximate:so that:
PE_{grav} | - G | ||
= | - G + mh | ||
= | constant + mgh. | (27) |
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