Gravity

Dr. Pamela Gore
Georgia Perimeter College

Objectives

Discuss the force that governs the motions in the solar system.
Discuss the contributions of Sir Issac Newton to the theory of universal gravitation.
State Newton's three laws of motion, and tell what they have to do with gravity.
Explain the concept of mass.
Explain the various things that are involved in the formula for Newton's Universal Law of Gravitation.

This section addresses, in whole or in part, the following Georgia GPS standard(s):

S6E1e. Explain that gravity is the force that governs the motion in the solar system.

This section addresses, in whole or in part, the following Benchmarks for Scientific Literacy:

Every object exerts gravitational force on every other object. The force depends on how much mass the objects have and on how far apart they are. The force is hard to detect unless at least one of the objects has a lot of mass.
The sun's gravitational pull holds the earth and other planets in their orbits, just as the planets' gravitational pull keeps their moons in orbit around them.
Things on or near the earth are pulled toward it by the earth's gravity.
Everything on or anywhere near the earth is pulled toward the earth's center by gravitational force.
Isaac Newton created a unified view of force and motion in which motion everywhere in the universe can be explained by the same few rules. His mathematical analysis of gravitational force and motion showed that planetary orbits had to be the very ellipses that Kepler had proposed two generations earlier.
Newton's system was based on the concepts of mass, force, and acceleration, his three laws of motion relating them, and a physical law stating that the force of gravity between any two objects in the universe depends only upon their masses and the distance between them.
The Newtonian model made it possible to account for such diverse phenomena as tides, the orbits of planets and moons, the motion of falling objects, and the earth's equatorial bulge.

This section addresses, in whole or in part, the following National Science Education Standards:

Gravity is the force that keeps planets in orbit around the sun and governs the rest of the motion in the solar system. Gravity alone holds us to the earth's surface and explains the phenomena of the tides.

Introduction to Gravity

Gravity holds us to the Earth's surface. Everything on or anywhere near the Earth is pulled toward the Earth's center by gravitational force.

The sun's gravitational pull holds the Earth and other planets in their orbit. The gravitational pull of planets keeps their moons in orbit around them.

The gravitational pull of the Moon and the Sun causes the tides in the ocean. Oceanic tidal range varies from place to place on the Earth. In some places, the tidal range is less than 2 meters (6 feet). In other places, namely the Bay of Fundy in Nova Scotia, the tidal range is as much as 16 meters (52.5 feet). The tides rise and fall every 12 hours and 25 minutes.

There is also a phenomenon called "Earth tides". The Earth's solid surface is pulled and distorted by the gravitational pull of the Moon and the Sun. Solid Earth tides can cause the surface of the Earth to rise and fall by several centimeters. Studies in Oklahoma have discovered a cyclic variation in gravity that oscillates over a period of about 12 hours, due to the tidal gravitational pull of the Moon and the Sun.

Gravity - The contributions of Isaac Newton (1642-1727)

By the time Sir Isaac Newton had entered Cambridge University in 1661, the scientific world had accepted the heliocentric (sun-centered) model for the solar system. Kepler had produced a mathematical theory for planetary motions, and Galileo had supplied observational evidence from his research with the telescope.

Questions still remained. What was the force that caused the planets to move as they do around the Sun? Why does the Moon orbit the Earth?

Newton found answers to these questions.

In 1665, a plague in London caused Cambridge Univ. to be closed; everyone was sent home. Newton had a long vacation and set out to study the force that holds the planets captive to the sun.

Newton's Three Laws of Motion:

Every object remains at rest or moves at a constant speed in a straight line unless an unbalanced external force acts on it.
The acceleration "a" produced by an applied force "F" on an object of mass "m" is
a = F/m
or F=ma
If an object exerts a force on another object, the second object exerts an equal and opposite force on the first; action = reaction. (Every action has an equal and opposite reaction.)

Newton invented calculus to prove his ideas. Planets orbit the sun in curved paths. Newton deduced that a force was acting on the planets. If no force was present, planets would travel in straight lines.
The force is directed toward the Sun (like swinging a ball on a string).

Newton's Law of Universal Gravitation

Mass = a quantity of matter.
The more mass an object has, the harder it is to move.
More force is needed to give the same acceleration to a more massive object. Twice the mass requires twice the force.

The Sun is much more massive than the planets. Both feel the same force, but the planets have greater accelerations.

The force of gravity is proportional to the mass of the sun times the mass of the planet.

The force diminishes with distance - The force is inversely proportional to the square of the planet's distance from the Sun (d).

Force of gravity "F" is proportional to 1/d².

For a large spherical mass (like Sun, planet), the force can be considered as concentrated at their centers.

Mathematical expression for the force acting between planets and the Sun:

F = G (mass of Sun) (mass of planet) / d²

Note that G is a gravitational constant.

Newton's Law of Universal Gravitation.
The force of attraction between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Newton calculated the gravitational acceleration at the distance of the moon and compared it to the moon's actual orbital acceleration. The actual value = the predicted value!

This proved that gravity maintains the moon in its orbit.

Hence, the force of gravity explains the motions of the planets. The Sun's gravitational force prevents the planets from moving in straight lines.

Question:
The Sun has a mass of 2x10³⁰ kg, and is 1.5x10⁸ km away, while the mass of the Moon is 7.35x10²² kg, and is 3.8x10⁵ km away. Which exerts a stronger gravitational influence on the Earth?

Answer:
The Sun.

Remember:
Obey gravity. It's the Law!

Gravity - It's not just a good idea, it's the Law.

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Page created by Pamela J.W. Gore
Georgia Perimeter College,
Clarkston, GA

Page created March 30-31, 2005