Gravity

# Gravity - Gravitation The property of all objects in the...

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Unformatted text preview: Gravitation The property of all objects in the universe which carry mass, by virtue of which they attract one another, is called Gravitation. Centripetal Acceleration of the Moon Newton, after determining the centripetal acceleration of the moon, formulated the law of universal gravitation. Suppose that the moon is orbiting around the earth in a circular orbit. If V = velocity of the moon in its orbit, Rm = distance between the centres of earth and moon, T = time taken by the moon to complete one revolution around the earth. For determining the centripetal acceleration of the moon,. Newton applied Huygen's formula which is a(c) = v2 / r For moon, am = v2 / Rm ..................... (1) But v = s/t = circumference / time period = 2 Rm/T π Therefore, v2 = 4 2Rm2 / T2 π Therefore, => a(m) = (4 2Rm2/T2) x (1/Rm) π a(m) = 4 2Rm / T2 π Put Rm = 3.84 x 10(8) m T = 2.36 x 10(6) sec Therefore, a(m) = 2.72 x 10(-3) m/s2 Comparison Between 'am' AND 'g' Newton compared the centripetal acceleration of the moon 'am' with the gravitational acceleration 'g'. i.e., am / g = 1 / (60)2 ................. (1) If Re = radius of the earth, he found that Re2 / Rm2 - 1 / (60)2 ......................... (2) Comparing (1) and (2), am / g = Re2 / Rm2 ..................................... (3) From equation (3), Newton concluded that at any point gravitational acceleration is inversely to the square of the distance of that point from the centre of the earth. It is true of all bodies in the universe. This conclusion provided the basis for the Newton' Law of Universal Gravitation. @import "/extensions/GoogleAdSense/GoogleAdSense.css"; Newton's Law of Universal Gravitation Consider tow bodies A and B having masses mA and mB respectively. Diagram Coming Soon Let, F(AB) = Force on A by B F(BA) = Force on B by A r(AB) = displacement from A to B r(BA) = displacement from B to A r(AB) = unit vector in the direction of r(AB). r(BA) = unit vector in the direction of r(BA). From a(m) / g = Re2 / Rm2, we have F(AB) ∞ 1 / r(BA)2 ......................... (1) Also, F(AB) ∞ m(A) ............................... (2) F(BA) ∞ m(B) According to the Newton's third law of motion F(AB) = F(BA) .................... (for magnitudes) F(AB) = F(BA) ....
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Gravity - Gravitation The property of all objects in the...

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