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1. In Newton's late 17th century era, there were relatively accurate estimates, from terrestrial and astronomical observations and experiments, of the distance of the Earth to the Sun (drs = 150 million kilometers) and the circumference of the Earth (Ce = 40,000 kilometers [the meter was later defined during the late 18th century French revolution in relation to the size of the Earth]). Newton further estimated, likely based on the density of rocks, that the Earth was a solid sphere with a density about 6 times the density of water, which has density of pwater = 1 g/cm³. A) Based on these estimates, what is the mass of the Earth Mg? B) From Newton's 2nd law, what is the magnitude of the force on a 1 kg mass falling freely near the surface of the Earth? C) The force in B) is due to Earth's gravity, which from Newton's law of universal law of mME gravitation is given by FG = G where the radius of the Earth RE serves as the distance Rg2 between the two masses. Use this formula, the result in B), the mass of the Earth from A), and the estimates above to deduce a value for the universal constant G. Check that it reasonably agrees with the modern "textbook" value.

1. In Newton's late 17th century era, there were relatively accurate estimates, from terrestrial and astronomical observations and experiments, of the distance of the Earth to the Sun (drs = 150 million kilometers) and the circumference of the Earth (Ce = 40,000 kilometers [the meter was later defined during the late 18th century French revolution in relation to the size of the Earth]). Newton further estimated, likely based on the density of rocks, that the Earth was a solid sphere with a density about 6 times the density of water, which has density of pwater = 1 g/cm³. A) Based on these estimates, what is the mass of the Earth Mg? B) From Newton's 2nd law, what is the magnitude of the force on a 1 kg mass falling freely near the surface of the Earth? C) The force in B) is due to Earth's gravity, which from Newton's law of universal law of mME gravitation is given by FG = G where the radius of the Earth RE serves as the distance Rg2 between the two masses. Use this formula, the result in B), the mass of the Earth from A), and the estimates above to deduce a value for the universal constant G. Check that it reasonably agrees with the modern "textbook" value.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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1. In Newton's late 17th century era, there were relatively accurate estimates, from terrestrial and astronomical observations and experiments, of the distance of the Earth to the Sun (dEs = 150 million kilometers) and the circumference of the Earth (Ce = 40,000 kilometers [the meter was later defined during the late 18th century French revolution in relation to the size of the Earth]). Newton further estimated, likely based on the density of rocks, that the Earth was a solid sphere with a density about 6 times the density of water, which has density of pwater = 1 g/cm³. A) Based on these estimates, what is the mass of the Earth Mp? B) From Newton's 2nd law, what is the magnitude of the force on a 1 kg mass falling freely near the surface of the Earth? C) The force in B) is due to Earth's gravity, which from Newton's law of universal law of gravitation is given by FG = G2, where the radius of the Earth RĘ serves as the distance mMg RE between the two masses. Use this formula, the result in B), the mass of the Earth from A), and the estimates above to deduce a value for the universal constant G. Check that it reasonably agrees with the modern “textbook" value.
Transcribed Image Text:1. In Newton's late 17th century era, there were relatively accurate estimates, from terrestrial and astronomical observations and experiments, of the distance of the Earth to the Sun (dEs = 150 million kilometers) and the circumference of the Earth (Ce = 40,000 kilometers [the meter was later defined during the late 18th century French revolution in relation to the size of the Earth]). Newton further estimated, likely based on the density of rocks, that the Earth was a solid sphere with a density about 6 times the density of water, which has density of pwater = 1 g/cm³. A) Based on these estimates, what is the mass of the Earth Mp? B) From Newton's 2nd law, what is the magnitude of the force on a 1 kg mass falling freely near the surface of the Earth? C) The force in B) is due to Earth's gravity, which from Newton's law of universal law of gravitation is given by FG = G2, where the radius of the Earth RĘ serves as the distance mMg RE between the two masses. Use this formula, the result in B), the mass of the Earth from A), and the estimates above to deduce a value for the universal constant G. Check that it reasonably agrees with the modern “textbook" value.
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