“Pick a flower on Earth and you move the farthest star.” Paul Dirac, English Physicist

Newton’s Universal Law of Gravitation

The Gravitational Force Newton’s Universal Law of Gravitation states that every particle in the universe exerts an attractive force on every other particle. Where “G” is the “universal gravitational constant” G = 6.67 x 10-11

What happens to the Force if one of the masses is doubled? It is also doubled. What happens to the Force if both of the masses were doubled? It will be four times larger. What happens to the Force if one of the masses is doubled and then other one is halved? The Force will remain the same.

This is an “inverse square” law, since the Force is proportional to the inverse of the distance squared. Example: At twice the distance, the gravitational force between two objects would be less. How much less?

What if the distance was 4d? 4 times the original force Two objects are separated by some distance, d. How would the gravitational force differ if the distance was tripled? 1/9 the original force What if the distance was 4d? 1/16 the original force 5d? 10d? ½ d? 4 times the original force

Example: Two masses of 8 kg and 12 kg are separated by 1. 5 m Example: Two masses of 8 kg and 12 kg are separated by 1.5 m. What is the gravitational force they exert on each other? How do you enter all those numbers in your calculator? Use your exponent button for “G”!! 6.67E-11*8*12÷(1.52) = F = 2.85 x 10-9 N G = 6.67 x 10-11

What is the gravitational force between a 600 kg mass and a 850 kg mass if they are 0.4 meters apart? F = 2.126 x 10-4 N G = 6.67 x 10-11

Example: Two masses of 3 x 103 kg and 1.8 x 1015 kg are separated by d = 1.4 x 1021m. What is the gravitational force they exert on each other? How do you enter all those numbers in your calculator? Use your exponent button!! 6.67E-11*3E3*1.8E15÷1.4E21 2 = F = 1.84 x 10-34 N G = 6.67 x 10-11

What’s the shortcut to get d2 out of the denominator? If the gravitational force between a 75 kg mass and a 120 kg mass is 4.2 x 10-4N, how far apart are they? What’s the shortcut to get d2 out of the denominator? Trade places with F!! d = 0.0378 m G = 6.67 x 10-11

Finding “g” Weight is the gravitational force a planet exerts. Weight = Gravitational Force mg = G “g”, the acceleration due to gravity can be found by canceling an “m”. The distance, d, is measured from the center of the planet to the location of interest. (often, the radius) The acceleration due to gravity, “g”, is also called the “gravitational field strength”. planet

How large is “g” on the planet Venus, which has a mass of 4 How large is “g” on the planet Venus, which has a mass of 4.87 x 1024 kg and has a radius of 6,050,000 meters? 6.67E -11x 4.87 E24 ÷ 6,050,0002 = g = 8.87 m/s2

Example: An asteroid of radius 500 m has a mass of 6. 5 x 1013 kg Example: An asteroid of radius 500 m has a mass of 6.5 x 1013 kg. What is the gravitational field strength at its surface? 6.67E -11 x 6.5 E13 ÷ 5002 = g = 0.0173 m/s2

Aristotle Geocentric universe 384 BC “geocentric” – Earth centered universe…… WRONG!

Ptolemy, 83 AD Ptolemy (also geocentric universe) presented his astronomical models in convenient tables, which could be used to compute the future or past position of the planets, the Sun, and Moon, the rising and setting of the stars, and eclipses of the Sun and Moon. His model showed the planets turning in small circles called “epicycles” as they orbited the Earth! The tables actually produced fairly good predictions, but his model and his geocentric universe was….. WRONG! Ptolemy was also the first to use latitude and longitude lines.

Copernicus 1473 heliocentric universe “sun-centered” universe Although others before him had proposed that the planets orbit the sun rather than the Earth, Copernicus was the first to publish mathematical evidence

Tycho Brahe 1546-1601 Cataloged over 20 yrs of observations Had an accident in a duel Died a mysterious death… Tycho Brahe 1546-1601

A mathematician hired as Brahe’s assistant Johannes Kepler 1571 A mathematician hired as Brahe’s assistant Wrote Three Laws of Planetary Motion

Kepler’s First Law The Law of Orbits: All planets have elliptical orbits with the sun at one focus. Perihelion – point on ellipse closest to orbited body Aphelion – point on ellipse farthest from orbited body

Earth’s orbit is almost circular

Planets’ orbits are only slightly elliptical Comets have highly elliptical orbits

Kepler’s Second Law 2. The Law of Areas: A line that connects a planet to the sun sweeps out equal areas in equal times. (Planets move faster when they are closer to the sun.)

Kepler’s Third Law 3. The Law of Periods: The square of the period of a planet is proportional to the cube of its average orbital radius. (earth years) T2 = r3 (AU) An AU is an “astronomical unit” and is the distance from the Sun to the Earth.

Venus is located 0. 72 AU’s from the Sun Venus is located 0.72 AU’s from the Sun. How many years does it take Venus to orbit the sun? T2 = a3 Math button or use housetop X cubed 0.61 years

If it takes an asteroid 5 Earth years to orbit the sun, how far is the asteroid from the sun? Math button cube root 2.92 AU

Improved the military spyglass to observe the sky, known as telescope Galileo 1564-1642 Improved the military spyglass to observe the sky, known as telescope Saw moons of Jupiter, Venus phases, sunspots, mountains on moon

Sir Isaac Newton 1642 Said that gravity was not just an Earthly force, but a Universal force. Wrote the Universal Law of Gravitation

Henry Cavendish October 1731 - February 1810 Cavendish is known for the Cavendish experiment, the first to measure the force of gravity between masses in a laboratory and to produce an accurate value for Earth's density. His work led others to accurate values for the gravitational constant (G) and Earth's mass. He is also responsible for the relationship between electric potential and current, now called Ohm's Law

Cavendish Experiment 1797 Lord Henry Cavendish experimentally determined the value of G using a torsion balance Torsion Balance 6 ft long – light rigid rod Two metal spheres were attached to each end Rod was suspended by wire

Albert Einstein 1879 The effects of gravity are just the results of the distortion of the “fabric of space-time” or the “space-time continuum” Predicted gravitational lensing Gravity is not really a “force” at all!