Retrograde Motion, Triangulation

1
Retrograde Motion, Triangulation Conclusion
Part I
2
Naked-Eye Observation of the Planets

• The planets change their position with respect to
  the stars
• The planets, unlike the Sun and the Moon, show
  retrograde motion
• The planets get brighter and dimmer
• They are brightest when they are in retrograde
  motion
• This must mean that they are closest to us at
  this point (Why?)

3
What can we conclude from observing patterns in
the sky?

• Earth OR Celestial Sphere rotates
• Earth rotates around the Sun OR Sun moves about
  Earth
• Moon rotates around the Earth or v.v.?
• Must be former, due to moon phases observed!
• Size of the earth from two observers at different
  locations
• Size of moon moons orbit from eclipses

4
Performing Experiments

• Experiments must be repeatable requires careful
  control over variables
• Possible outcomes of an experiment
• The experiment may support the theory
• We then continue to make predictions and test
  them
• The experiment may falsify the theory
• We need a new theory that describes both the
  original data and the results of the new
  experiment
• Since we cannot do every possible experiment, a
  theory can never be proven true it can only be
  proven false

5
Astronomical Distance Measurements

• Fundamental technique uses triangulation
• Objects appear to move with respect to background
  if looked at from different vantage points
• Try looking at you thumb with only your left,
  then right eye
• The more the thumb jumps, the closer it is!
• Measure jump, get distance
• See Link, Link 2

Liu Hui, How to measure the height of a sea
island.
6
Simple Triangulation

• Use geometry of similar triangles
• You know everything about a triangle if you know
• Two sides and an angle
• One side and two angles
• Example baseline 100ft, angles 90 and 63.4
  then distance (100ft)(tan 63.4) 200ft

7
Parallax Basics

• The closer the object, the bigger the parallax
  (or parallactic angle)
• Pencil held close (solid lines)
• Pencil held far (dashed lines)
• The farther the object the harder to measure the
  small angle, the more uncertain the distance

8
Triangulating the Size of the Earth

• Eratosthenes (ca. 276 BC)
• Measures the radius of the earth to about 20

9
Calculation

• Angle is measured to be 7.2 360/50
• So distance Alexandria-Syene is 1/50 of Earths
  circumference
• Baseline can be measured 5000 stades
• ? Circumference is 23,330 miles (modern value
  25,000 miles only 7 off

10
Baseline Bigger Better

• Can use Earths large size for a 12,700km
  baseline
• Just wait 12 hours!

11
Counterargument or not?

• Objection to Aristarchuss model of a moving
  Earth parallax of stars is not observed (back
  then)
• Aristarchus argued (correctly) that this means
  the stars must be very far away

12
Distances to the Stars

• Use even bigger baseline by waiting ½ year, not ½
  day
• Baseline 300 million km Parallax can be used out
  to about 100 light years
• The bigger the parallactic angle, the closer the
  star!
• A star with a measured parallax of 1 is 1 parsec
  away
• 1 pc is about 3.3 light years
• The nearest star (Proxima Centauri) is about 1.3
  pc or 4.3 lyr away

13
The most important measurement in Astronomy
Distance!

• The distances are astronomical of course
• The distance scales are very different
• Solar system light minutes
• Stars light years
• Galaxies 100,000 ly
• Universe billions of ly
• Need different yardsticks

14
Yardsticks and the Expanding Universe

• Realizing (measuring) the distances to objects
  means realizing how big the universe is
• We realized that the solar system is not the
  universe
• We realized that our galaxy is not the universe
• We realized that the universe is not static