In the law of universal gravitation, Newton assumed that the force was proportional to the product of the two masses ( ∼ m 1 m 2 ) . While all scientific conjectures must be experimentally verified, can you provided arguments as to why this must be? (You may wish to consider simple examples in which any other form would lead to contradictory results.)
In the law of universal gravitation, Newton assumed that the force was proportional to the product of the two masses ( ∼ m 1 m 2 ) . While all scientific conjectures must be experimentally verified, can you provided arguments as to why this must be? (You may wish to consider simple examples in which any other form would lead to contradictory results.)
In the law of universal gravitation, Newton assumed that the force was proportional to the product of the two masses
(
∼
m
1
m
2
)
. While all scientific conjectures must be experimentally verified, can you provided arguments as to why this must be? (You may wish to consider simple examples in which any other form would lead to contradictory results.)
In the law of universal gravitation, Newton assumed that the force was proportional to the product of the two masses ( ~m1 m2 ). While all scientific conjectures must be experimentally verified, can you provide arguments as to why this must be? (You may wish to consider simple examples in which any other form would lead to contradictory results.)
In the law of universal gravitation, Newton assumed that the force was proportional to the product of the two masses (~m1m2). While all scientific inferences must be experimentally verified, can you provide arguments as to why this must be correct?
In this problem, you are going to explore three different ways to determine the gravitational constant G.
a) By observing that the centripetal acceleration of the Moon around the Earth is ac = 2.66 × 10-3 m/s2, what is the gravitatonal constant G, in cubic meters per kilogram per square second? Assume the Earth has a mass of ME = 5.96 × 1024 kg, and the mean distance between the centers of the Earth and Moon is rm = 3.81 × 108 m.
b) Measuring the centripetal acceleration of an orbiting object is rather difficult, so an alternative approach is to use the period of the orbiting object. Find an expression for the gravitational constant in terms of the distance between the gravitating objects rm, the mass of the larger body (the earth) ME, and the period of the orbiting body T.
c) The gravitational constant may also be calculated by analyzing the motion of an object, launched from the surface of the earth at an initial velocity of vi. Find an expression of the gravitational constant…
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