Gravity Newton’s Law of Gravitation Gravitational Fields

Newton’s Law of Gravitation m1m1 m2m2 r There is a force of gravity between any pair of objects anywhere. The force is proportional to each mass and inversely proportional to the square of the distance between the two objects. Its equation is: F G = G m 1 m 2 r 2r 2 The constant of proportionality is G, the universal gravitation constant. G = 6.67 · N·m 2 / kg 2. Note how the units of G all cancel out except for the Newtons, which is the unit needed on the left side of the equation.

Early Astronomers In the 2 nd century AD the Alexandrian astronomer Ptolemy put forth a theory that Earth is stationary and at the center of the universe and that the sun, moon, and planets revolve around it. Though incorrect, it was accepted for centuries. In the early 1500’s the Polish astronomer Nicolaus Copernicus boldly rejected Ptolemy’s geocentric model for a heliocentric one. His theory put the sun stated that the planets revolve around the sun in circular orbits and that Earth rotates daily on its axis. In the late 1500’s the Danish astronomer Tycho Brahe made better measurements of the planets and stars than anyone before him. The telescope had yet to be invented. He believed in a Ptolemaic-Coperican hybrid model in which the planets revolve around the sun, which in turn revolves around the Earth.

Early Astronomers In the late 1500’s and early 1600’s the Italian scientist Galileo was one of the very few people to advocate the Copernican view, for which the Church eventually had him placed under house arrest. After hearing about the invention of a spyglass in Holland, Galileo made a telescope and discovered four moons of Jupiter, craters on the moon, and the phases of Venus. The German astronomer Johannes Kepler was a contemporary of Galileo and an assistant to Tycho Brahe. Like Galileo, Kepler believed in the heliocentric system of Copernicus, but using Brahe’s planetary data he deduced that the planets move in ellipses rather than circles. This is the first of three planetary laws that Kepler formulated based on Brahe’s data. Both Galileo and Kepler contributed greatly to work of the English scientist Sir Isaac Newton a generation later.

Kepler’s Laws of Planetary Motion 1. Planets move around the sun in elliptical paths with the sun at one focus of the ellipse. 2. While orbiting, a planet sweep out equal areas in equal times. 3. The square of a planet’s period (revolution time) is proportional to the cube of its mean distance from the sun: T 2  R 3 Here is a summary of Kepler’s 3 Laws: These laws apply to any satellite orbiting a much larger body.

Uniform Gravitational Fields We live in what is essentially a uniform gravitational field. This means that the force of gravity near the surface of the Earth is pretty much constant in magnitude and direction. The green lines are gravitational field lines. They show the direction of the gravitational force on any object in the region (straight down). In a uniform field, the lines are parallel and evenly spaced. Earth’s surface continued on next slide

Uniform Gravitational Fields (cont.) Earth’s surface 10 kg 98 N A 10 kg mass is near the surface of the Earth. Since the field strength is 9.8 N / kg, each of the ten kilograms feels a 9.8 N force, for a total of 98 N. So, we can calculate the force of gravity by multiply mass and field strength. This is the same as calculating its weight ( W = mg ).

Nonuniform Gravitational Fields Near Earth’s surface the gravitational field is approximately uniform. Far from the surface it looks more like a sea urchin. Earth The field lines are radial, rather than parallel, and point toward center of Earth. get farther apart farther from the surface, meaning the field is weaker there. get closer together closer to the surface, meaning the field is stronger there.