Newton's law of universal gravitation states that the (magnitude of the) gravitational force F be- tween two objects is given by mim2 F =G where G is the gravitational constant, m1, m2 are the masses of the two objects, and r is the distance between the objects. Here G = 6.674 · 10-11 m°kg-s2. A team of amateur astronomers have estimated that mị = 2. 1024 kg, m2 of 1% in each measurement. Use differentials to estimate the maximum relative error (in percent) when the force F is calculated from these measurements. 5- 1023 kg, and r = 1010 m, with a maximum relative error

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8. Newton's law of universal gravitation states that the (magnitude of the) gravitational force F be-
tween two objects is given by
F = G
mim2
%3D
where G is the gravitational constant, m1, m2 are the masses of the two objects, and r is the distance
between the objects. Here G = 6.674 · 10-11 m°kg's2. A team of amateur astronomers have
estimated that mi = 2. 1024 kg, m2 = 5- 1023 kg, and r =
of 1% in each measurement. Use differentials to estimate the maximum relative error (in percent)
when the force F is calculated from these measurements.
1010 m, with a maximum relative error
%3D
Transcribed Image Text:8. Newton's law of universal gravitation states that the (magnitude of the) gravitational force F be- tween two objects is given by F = G mim2 %3D where G is the gravitational constant, m1, m2 are the masses of the two objects, and r is the distance between the objects. Here G = 6.674 · 10-11 m°kg's2. A team of amateur astronomers have estimated that mi = 2. 1024 kg, m2 = 5- 1023 kg, and r = of 1% in each measurement. Use differentials to estimate the maximum relative error (in percent) when the force F is calculated from these measurements. 1010 m, with a maximum relative error %3D
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