Planetary Motion

1
Planetary Motion

• Planets move relative to stars
• motion is odd as sometimes East to West but
  occasionally West to East against the background
  of stars (E to W called retrograde motion)
• Historically large problem explaining planets
  motion

2
Models of the Solar System

• Ptolemaic - Geocentric
• Earth at center and motionless
• Sun and other planets orbit the Earth on circles
  within circles.

Mars
epicycle
Earth
deferent

• Stars also orbit Earth on very distant celestial
  sphere

3
Copernican - Heliocentric

• Sun at center
• All planets move about Sun on epicycles (circles
  on circles)
• Earth revolves on axis once per day
• Catholic Church adopts Ptolemaic as revealed
  truth in 13th Century. Copernican model
  published in 1543 with detailed comparisons to
  observations (after NC death so Church would not
  punish him)

4
Other Models

• Tycho Brahes - Earth at center but other planets
  orbit the Sun (effectively the same as
  Copernican)
• Keplers - Sun at center with planets orbitting
  the Sun in elliptical paths CORRECT
• Differentiate models by comparing predictions
  with observations
• SCIENTIFIC METHOD
• need best observations as possible

5
Observations of Brahe and Analysis of Kepler

• Brahe led team which collected data on position
  of planets (1580-1600 no telescopes)
• Kepler (mathematician) hired by Brahe to analyze
  data. Determined 3 Laws of planetary motion
  (1600-1630)
• Input - 20 years of data on
• angular position of planets
• approximate distances from Earth (accurate
  relative distances)
• Few modern tools (no calculus, no graph paper,
  no log tables)

6
Triangles and Parallax

• A triangle is determined by the length of the
  base and the opposite angle.
• If the base is fixed, the height is measured by
  the angle.
• Use to measure distances to planets and stars

base
angle A
angle B
7
Measuring Triangles

• How can the measurement of the triangle be
  improved?
• 1. Make the base larger
• 2. Measure the angle more accurately (for
  example, use a telescope)

8
Apparent Shift Parallax

• A moving observer sees fixed objects move.
• Near objects appear to move more than far objects
• The effect is due to the change in observation
  point, and is used by our eyes for depth
  perception.

Geocentric parallax
angle A
Earth
angle B
9
Shifting Stars

• The orbit of the earth is used as the base.
• Near stars appear to move more than far stars.

December
site A
Sun
site B
June
10
Stellar Parallax

• A photo of the stars will show the shift.

site A
site B
11
Sources of Parallax

• Heliocentric parallax uses the sun as a base.
• Take a photo at two different seasons.
• Geocentric parallax uses the earth as a base.
• Take a photo two times in one night.
• Use for planets

12
Keplers Laws of Planetary Motion (1630)

• FIRST LAW The orbit of a planet is an ellipse
  with the sun at one focus.

A line connecting the two foci in the ellipse
always has the same length.
13
Keplers Second Law

• The line joining a planet and the sun sweeps
  equal areas in equal time.

The planet moves slowly here.
The planet moves quickly here.
14
Keplers Third Law

• The square of a planets period is proportional
  to the cube of the length of the orbits
  semimajor axis.
• Mathematically, T2/a3 constant.(1 if use 1
  Earth year and 1 AU as units)
• The constant is the same for all objects orbiting
  the Sun.

direction of orbit
semimajor axis a
The time for one orbit is one period T