ASTRON 1142 Study Guide - Fall 2018, Comprehensive Midterm Notes - Earth, Sun, Orbit
12 Oct 2018
School
Department
Course
Professor
ASTRON 1142
MIDTERM EXAM
STUDY GUIDE
Fall 2018
Johannes Kepler and Kepler’s Law
Began with the scientific method
1. Observation: Obtained data about the universe and the big bang
2. Hypothesize: Form a hypothesis about the generation and age of the universe by
assuming since the universe started at one point, nothing could be older than the
time it would take to expand from that point.
3. Deduction: Use that hypothesis to make a prediction about the results of the
research. I.e. “the milky way galaxy will be X years old because we are Y km
away from the big bang and moving at a rate of Z km/sec.
4. Test: Test the prediction through formulas and other scientific theories.
Kepler’s 1st law of planetary motion
● The orbits of the planets are ellipses with the sun as the central focus
● Ellipses are characterized by two numbers:
○ Semimajor Axis: (a) size of the longest axis
○ Eccentricity: (e) shape of the ellipse (deviation from a perfect circle)
■ Perfect circle would have eccentricity of 0
● Orbit of Mars: a = 1.5237 e = 0.0934
Kepler’s 2nd Law of Planetary Motion
● The line joining the Sun and the planet sweeps out equal areas in equal times
○ Planets move fastest at Perihelion (Closest point to the sun)
○ Planets move slowest at Aphelion (Farthest point from the sun)
● Kepler’s 2nd Law provides a geometric description of the change in speed
○ Planets have to have the same area of their triangle with points A=Starting
Point, B=Sun location, C=Ending point for the same amount of travel time
Kepler’s 3rd Law of Planetary Motion
find more resources at oneclass.com
find more resources at oneclass.com
Isaac Newton and Physical Laws
Mass vs Weight
Mass: property that determines an object’s resistance to acceleration by forces and the
strength of its mutual gravitational attraction to other objects.
Weight: the force on an object due to gravity
W = mg = mGM/r^2 g = GM/r^2 g = 9.8m/s^2 on the surface of Earth
I.e. A mass of 70 kg corresponds to a weight of 154 lbs on Earth, 140 lbs on Mars 58
lbs on the moon
● Gravitational force is often expressed relative to Earth’s
Earth and Gravitational Force
The Earth has an equatorial bulge due to rotation
g = GM/r^2
g = 9.78 m/s^2 at the equator (9.83m/s^2 at the poles)
Isaac Newton (1642-1727)
● Born in Woolsthorpe, England (rural)
○ To a widowed mother who later remarried after Isaac was born
○ Raised by his maternal grandmother instead of mother/stepdad
○ Grew up a solitary child, but was unfit to be a farmer
■ The rural setting of his childhood likely played a large role in this
ability to stick to himself
● As an adult Isaac was quiet, irascible, and solitary
○ Fearful/Paranoid that others would steal his work
● Graduated from Cambridge (England’s top academic university) in 1665
The Plague Years
● The Great Plague of London (1665-1666) closed Cambridge, which sent Newton
back to his home until the end
● During this break from school, Newton spent his time working and pondering.
However, he never published anything until years later
○ Invented the integral and differential calculus
○ Developed the binomial theorem
○ Started fundamental work on optics
○ Formulated his laws of motion and gravitation
Lucasian Professor
● At age 26 (1669), he became the second Lucasian Professor of Mathematics at
Trinity College, Cambridge
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
The milky way galaxy will be x years old because we are y km away from the big bang and moving at a rate of z km/sec: test: test the prediction through formulas and other scientific theories. The orbits of the planets are ellipses with the sun as the central focus. Semimajor axis: (a) size of the longest axis. Eccentricity: (e) shape of the ellipse (deviation from a perfect circle) Perfect circle would have eccentricity of 0. Orbit of mars: a = 1. 5237 e = 0. 0934. The line joining the sun and the planet sweeps out equal areas in equal times. Planets move fastest at perihelion (closest point to the sun) Planets move slowest at aphelion (farthest point from the sun) Kepler"s 2nd law provides a geometric description of the change in speed. Planets have to have the same area of their triangle with points a=starting. Point, b=sun location, c=ending point for the same amount of travel time.
