Gravity

Mom was healer that was accused of being a witch Dad left to become a mercenary Crippled by small pox as a child Wanted to be a minister Thrown out of Lutheran church

Johannes Kepler Lived around the time of Galileo Mathematician, Astronomer, Astrologer Biggest job: provide update astrological charts of the Emperor Rudolph II Copernican vs. Ptolemaic Model

Mars’ orbit not a circle Eyes are source of depth perception Sun rotates on an axis Moon is the cause of tides

Keplers Law’s

Keplers First Law: planet paths are not circles but an ellipses with the sun at one focus of the ellipse

Keplers First Law Elliptical Motion of Planets

Keplers Second Law: A line drawn from the sun to a planet sweeps out an equal area in an equal time period.

Kepler’s Second Law Equal area in equal time interval

                                                                               

Keplers Third Law: The square of the ratio of the period of two planetary orbits is equal to the cube of the ratio of their average distance to the sun. (T1/T2)2 = (R1/R2)3

                                                             (T1/T2)2 = (R1/R2)3

Example: Earth and Mars both orbit the sun Example: Earth and Mars both orbit the sun. If the Earth has an orbital period of 365 days and an orbital radius of 1.50 x 1011m and Mars has an orbital radius of 2.28 x 1011m . How long is a Martian year?

TEarth = 365 days REarth = 1.5 x 1011 m RMars = 2.28 x 1011 m TMars = ? T

Law of Universal Gravitation

Son of a farmer who hated farming No money for college Did work-study at Cambridge School taught Aristotle Preferred to read Copernicus, Galileo and Keplier

Introduce Infinitesimal Calculus Spectral Colors of White Light Laws of Motion Universal Law of Gravitation Philosophiae Naturalis Principia Mathematica

“Objects attract other objects with a force…” Philosophiae Naturalis Principia Mathematica

“Objects attract other objects with a force that is proportional to the product of their masses…” Philosophiae Naturalis Principia Mathematica

“Objects attract other objects with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them.” Philosophiae Naturalis Principia Mathematica

Newton’s Law of Universal Gravitation: Every body in the universe attracts every other body with a force that is directly proportional to the product of their masses and is inversely proportional to the square of the distance between their centers. Where: G Universal Gravitational Constant Equation:

m1 m2 F 2m1 m2 2F 2m2 2m1 4F 6F 2m2 3m1

same force, but different accelerations. Even though the masses may be different sizes, they exert the same amount of force on each other – this is because of Newton’s third law. F = ma F = ma same force, but different accelerations.

m1 m2 r F Inverse Square Law m1 m2 2r 1/4 F m1 m2 the greater the distance between the masses, the less the force between them 3r 1/9 F m1 m2 4F 1/2r

Example: Find the force of gravitational attraction between two students separated by 1.2 m. The masses of the students are 60 kg and 70 kg.

Weighing the Earth: Purpose: Use the Law of Universal Gravitation to determine the mass of the Earth. Let m1 = mass of object = mo m2 = mass of Earth = ME r = radius of Earth = RE = 6380 km = 6.380 x 106 m

Since Fg is the weight of the object, &

Also can find g at any height above a planet’s surface. Note: developed the equation: Or in general P : any planet Given the mass of any planet and its radius, the acceleration due to gravity on that planet can be found. Also can find g at any height above a planet’s surface. R= height + radius of the planet

Example: Find the value of g on Mars, using the information on pg 173.

What is g 1000 km above the surface of mars?

1 AU: (Astronomical Unit) average distance from earth to the sun 149,597,870.7 km 92,955,807.27 miles Mercury 0.387 Venus 0.723 Earth 1 (of course) Mars 1.52 Jupiter 5.20 Saturn 9.54 Uranus 19.2 Neptune 30.1 Pluto 39.4

1 parsec: One parsec is approximately 3.262 light-years The nearest known star to the Earth, other than the Sun, is Proxima Centauri 1.29 parsecs away. The center of the Milky Way is about 8 kpc from the Earth, and the Milky Way is about 30 kpc across. The Andromeda Galaxy (M31) is slightly less than 800 kpc away from the Earth.