GVY - Introduction to Gravity

Gravity Overview

Introduction

One of the most successful laws in the history of science is Newton's universal law of gravitation, both in terms of its descriptive power as well as its ability to predict. Just prior to Newton, Copernicus cataloged enormous detail about the movement of celestial bodies, followed by Kepler discovering empirical mathematical relationships. Using the second law, Newton put these observations and relationships on solid mathematical footing, discovering a constant that describes forces that result from mass anywhere in the universe. Newton's discovery of this law is so successful in estimating the masses of planets and their orbital motions that 150 years after Newton published this law, anomalies in the orbits of planets had the appearance of disobeying this law. This led astronomers to hypothesize the presence of a previously undiscovered planet. If Newton's Universal Law of Gravitation was to stand, there must have been an undiscovered mass leading to this anomaly. Turning their telescopes to where such a body must be to cause this led astronomers to the discovery of the planet Neptune.

Essential Questions

1. What is the law of universal gravitation?
2. What characteristic of matter causes a gravitational field?
3. Why does the gravitational field between two books on a table not cause them to slide together?
4. What are Kepler's three laws of orbital motion?
5. How can Kepler's third law be derived from Newton's second law?
6. Kepler's second law is a restatement of which conservation principle?
7. Since gravitational potential energy is mgh only near the surface of the earth, how is gravitational potential energy calculated when this assumption is violated?
8. How can the principle of conservation of energy be used far from the surface of a planet?
9. How is escape velocity calculated?

Key Terms

1. geosynchronous orbit - an orbit around the Earth with an orbital period of one day matching the Earth's rotation period, making the satellite appear stationary relative to a point on Earth.
2. inverse square law - any physical law stating that a specified physical quantity is inversely proportional to the square of the distance from the source of that physical quantity.
3. law of universal gravitation - the law which states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
4. polar orbit - an orbit in which a satellite passes above both poles of a planet, in a plane perpendicular to the equatorial plane.
5. satellite - a natural or man-made object in orbit around a planet.
6. superposition - for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually.
7. universal gravitation constant - a physical constant of proportionality between force and the ratio of the product of two masses to the square of the distance between the mass centers square (in the law of universal gravitation).
8. equipotential - a region in space where every point in it is at the same potential equivalent to a region of space where a given mass has a constant potential energy.
9. gravitational potential energy () - potential energy associated with the gravitational force, equal and opposite to the work required to elevate mass against a planet's  gravity.
10. gravitational potential (V) - gravitational potential energy per unit mass.
11. Kepler's Laws of Planetary Motion - three laws describing the orbits of planets developed by Johannes Kepler based on empirical observations of Tycho Brahe and others.

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