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I don't understand where g=6.667*10^-11N*m^2/kg^2 comes from. Can you help me understand how the book came up with that equatio

I don't understand where g=6.667*10^-11N*m^2/kg^2 comes from. Can you help me understand how the book came up with that equatio

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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I don't understand where g=6.667*10^-11N*m^2/kg^2 comes from.

Can you help me understand how the book came up with that equation?

9.2 The Universal Gravitational Constant, G The proportionality form of the universal law of gravitation can be expressed as an exact equation when the constant of proportionality G is introduced. G is called the universal gravitational constant. Then the equation is The units of G make the force come out in newtons. The magnitude of G is the same as the gravitational force between two 1-kilogram masses that are 1 meter apart: 0.0000000000667 newton. So G = 6.67 X 10-¹¹N•m²/kg² This is an extremely small number.³ It shows that gravity is a very weak force com- pared with electrical forces. The large net gravitational force we feel as weight is because of the enormous number of atoms in planet Earth that are pulling on us. Interestingly, Newton could calculate the product of G and Earth's mass, but not either one alone. G alone was first calculated by the English physicist Henry Cavendish in 1798, more than 70 years after Newton's death. m1m2 F = G- d² m1m₂ d² Cavendish measured G by measuring the tiny force between lead masses with an ex- tremely sensitive torsion balance, as Professor Brage shows in one of the opening photos at the beginning of this chapter. A simpler method was later developed by Philipp von Jolly, who attached a spherical flask of mercury to one arm of a sensitive balance (Fig- ure 9.4). After the balance was put in equilibrium, a 6-ton lead sphere was rolled be- neath the mercury flask. The gravitational force between the two masses was measured by the weight needed on the opposite end of the balance to restore equilibrium. All the quantities, m₁, m₂, F, and d, were known, from which the constant G was calculated: F G = 6.67 × 10-¹1 N/kg/m² = 6.67 x 10-¹¹ Nm²/kg² - 2 y FIGURE 9.3 As the rocket get the gravitational other decreases. Just as sheet r cian playing m a physics stuc stand how ca VIDEO: of Meas Betw
Transcribed Image Text:9.2 The Universal Gravitational Constant, G The proportionality form of the universal law of gravitation can be expressed as an exact equation when the constant of proportionality G is introduced. G is called the universal gravitational constant. Then the equation is The units of G make the force come out in newtons. The magnitude of G is the same as the gravitational force between two 1-kilogram masses that are 1 meter apart: 0.0000000000667 newton. So G = 6.67 X 10-¹¹N•m²/kg² This is an extremely small number.³ It shows that gravity is a very weak force com- pared with electrical forces. The large net gravitational force we feel as weight is because of the enormous number of atoms in planet Earth that are pulling on us. Interestingly, Newton could calculate the product of G and Earth's mass, but not either one alone. G alone was first calculated by the English physicist Henry Cavendish in 1798, more than 70 years after Newton's death. m1m2 F = G- d² m1m₂ d² Cavendish measured G by measuring the tiny force between lead masses with an ex- tremely sensitive torsion balance, as Professor Brage shows in one of the opening photos at the beginning of this chapter. A simpler method was later developed by Philipp von Jolly, who attached a spherical flask of mercury to one arm of a sensitive balance (Fig- ure 9.4). After the balance was put in equilibrium, a 6-ton lead sphere was rolled be- neath the mercury flask. The gravitational force between the two masses was measured by the weight needed on the opposite end of the balance to restore equilibrium. All the quantities, m₁, m₂, F, and d, were known, from which the constant G was calculated: F G = 6.67 × 10-¹1 N/kg/m² = 6.67 x 10-¹¹ Nm²/kg² - 2 y FIGURE 9.3 As the rocket get the gravitational other decreases. Just as sheet r cian playing m a physics stuc stand how ca VIDEO: of Meas Betw
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