Universal Law of Gravitation

Some Basics The force of gravity is the mutual attraction of objects to one another. The acceleration due to gravity (g) is rate at which an object falls near earth’s surface if gravity is the only force acting on them – Value of 9.8 m/s 2 on Earth regardless of mass

History of Gravity Kepler described planetary motion but did not explain why Newton came up with the idea of universal gravitation (all objects are attracted to one another) but…what accounts for differences such as – Apple falls towards earth at 9.8 m/s 2 – Moon falls towards earth at m/s 2 (this is the centripetal acceleration of the moon in orbit)

History Continued Newton reasoned that gravity must be “diluted” by distance. The distance from the center of the Earth to the center of the moon is 60 times that of the center of Earth to the apple so the force of attraction is 1/60 2 as much for the apple-Earth system There is an inverse square relationship connecting the distance between two objects and their mutual force of attraction

History continued Newton also knew that according to F=ma, the force of attraction between objects is directly proportional to their mass. Thus, Newton could conclude…

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The Proportionality Constant Just as radius is related to circumference by 2, gravitational force is related to mass and distance by a proportionality constant known as The Universal Gravitational Constant, G. G = X Nm 2 /kg 2

Cavendish G was first measured 150 years after Newton’s discovery of universal gravitation by an English physicist, Henry Cavendish. Cavendish accomplished this by measuring the tiny force between lead masses with an extremely sensitive torsion balance.

Gravity – A field force Objects with mass are responsible for a gravitational field around them. This field is the region of influence on other masses. Ultimately, the gravitational force felt by any other mass depends upon the strength of the field at its location The arrows in this picture represent the direction and relative strength of the field surrounding a mass

Gravitational Field Strength Gravitational field strength is defined as the amount of force per unit of mass at a given location in a gravitational field. Consider a satellite some distance from Earth: Earth The field strength of the Earth at the location of the satellite would be the ratio of gravitational force on the satellite to the mass of the satellite: F g m s Satellite

Using the Universal Law of Gravity Two students sit 1.5 m apart in the classroom. If the students have masses of 85 kg and 68 kg, what is the strength of the gravitational force between these students?

Using the Universal Law of Gravity What is the weight of an 80.0 kg person at the surface of the Earth? (R E = 6.38 x 10 6 m, M E = 5.98 x kg)

Using the Universal Law of Gravity What must be the speed of a satellite if it is to orbit the Earth at an altitude of 250 km?