Kepler’s Laws and Motion

Kepler’s Laws and Motion Astronomy 311 Professor Lee Carkner Lecture 5

Tycho and Kepler • Tycho Brahe • Johannes Kepler was Tycho’s assistant and he used Tycho’s data to formulate three laws of planetary motion

Kepler’s First Law • Planetary orbits are ellipses with the Sun at one focus

Kepler’s Second Law • The radius vector sweeps out equal area in equal times

Kepler’s Third Law P2=a3 • P = • a= the semimajor axis in Astronomical Units (1 AU is mean Earth-Sun distance)

Why Do Kepler’s Laws Work? • Kepler didn’t know why the planets moved • In the 17th-18th century Galileo and Newton would lay the foundations of physics

Aristotle’s Laws of Motion • Aristotle (384-322 BC) was for 2000 years the leading authority on everything • Earth and Water (tended to move down towards the center of the Earth) • Objects move with constant velocity and heavier objects fall faster • Aristotle’s ideas were accepted without testing them

Galileo’s Laws of Motion • Galileo (1564-1642) conducted experiments with balls of different materials and an inclined plane to learn about motion • Objects do not fall at a constant rate, they fall faster as time goes on • All objects accelerate at the same rate • He could not quite prove it with his equipment

Focus Focus Minor axis Major Axis 1 Sun 3 4 A12 A34 2 Comet

Newton’s Laws of Motion • Isaac Newton • Newton’s Laws are universal, they apply everywhere (on the Earth, in space, on the Moon …) • It is sometimes difficult to see Newton’s Laws in action because of friction, gravity, air resistance etc.

Newton’s First Law • Inertia -- • Friction sometimes makes this hard to see, think of objects in space or on a sheet of ice

Newton’s Second Law • Force -- equal to the product of mass and acceleration (change in velocity): F=ma • This is true even without gravity

Newton’s Third Law • Action/Reaction -- • Forces occur in pairs directed in opposite directions • sit in a chair and gravity pulls down and the chair pushes up

Newton’s Law of Universal Gravitation • Gravity -- F=Gm1m2/r2 • Every object in the universe attracts every other object

Another Look at Kepler’s Laws • We can now understand Kepler’s Laws in terms of Newton’s Laws • Why don’t the planets fly off into space? • Why don’t the planets fall into the Sun?

Orbits

Newton’s Versions of Kepler’s Law’s • Planets move faster when closest to the Sun because of conservation of angular momentum • Kepler: P2=k a3 • Newton: P2=[42/G(m1+m2)] a3

Science and Philosophy • Newton’s methods and attitudes defined science as something separate from philosophy • He used the language of mathematics rather than rhetoric

Next Time • Read 7.5-7.6

Summary • Kepler • Planetary orbits are ellipses • Planets sweep out equal areas in equal times • P2 = a3 • Galileo • all objects fall with uniform acceleration regardless of mass

Newton • Inertia -- an object in motion remains in motion • Force -- F=ma • Action/Reaction -- Every action has an equal and opposite reaction • Gravity -- F=Gm1m2/r2

Kepler’s Laws and Motion