gravf - that m 3 is present then adding the force on m 1 by...

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Gravitational force and field THEORY In the seventeenth century Isaac Newton proposed the universal law of gravitation , which states the gravitational force one point mass, M, exerts on another point mass, m, when the two are separated by a distance, r, has a magnitude : F = G M m / r 2 , [valid for point masses only !] where G = 6.67x10 -11 N-m 2 /kg 2 ( g !) is the universal law of gravitation constant. The direction of F is found by noting that gravity always attracts. Assuming r points away from M and connects to m, then F = – GMm/r 2 r /| r | Newton next wondered, how do you find the gravity force between objects that are not points (e.g., the force by the earth on an apple)? To answer this question he invented the integral calculus and the next principle below. To address what happens when greater than two point masses are present Newton postulated the principle of superposition , which states: The force on point mass, m 1 , by point masses, m 2 , and m 3 is found by finding the force on m 1 by m 2 using the above force equation and ignoring the fact
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Unformatted text preview: that m 3 is present, then adding the force on m 1 by m 3 ignoring the presence of m 2 . Thus the force on m 1 by N-1 other point masses is the vector sum: i = N F 1 = Σ i = 2 F 1i , where F 1i is the force on m 1 by m i . • The gravitational force accounts for the large-scale structure of the universe and serves as the foundation of astronomy. The gravitational field at a point in space is measured by placing a small test mass, m test , at that location and measuring the gravitational force experienced by the test mass, F on test mass : g ≡ F on test mass / m test , The total gravitational field is the vector sum of all fields present. • The gravitational field produced by a point mass, M, a distance r away follows, where again r points away from M: g = -(GM/r 2 ) r / | r | [point mass only!] • many times r / | r | ≡ e r defines a new unit vector that is radial from M. EXAMPLES [in class]...
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gravf - that m 3 is present then adding the force on m 1 by...

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