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 & moon’s 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
Or the experiment may be wrong!
Variables = the quantities on which the outcome of the experiment depends 4

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%
Hellenistic period: follows AtG’s conquests of Persia, Egypt, parts of India. Greek the international language of learning. Lasts until the Roman conquests (44BC—100AD)
At summer solstice. Angle measured to be about 7 deg = 1/50 circle, hence dist from Syene to Alex about 1/50 the circumference of the earth.

9. Calculation Angle is measured to be 7.2 = 360/50
So distance Alexandria-Syene is 1/50 of Earth’s circumference
Baseline can be measured: 5000 stades
 Circumference is 23,330 miles (modern value: 25,000 miles – only 7% off
Calculation

10. Baseline: Bigger = Better
Can use Earth’s large size for a 12,700km baseline
Just wait 12 hours!

11. Counterargument or not?
Objection to Aristarchus’s 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
Parallax was first measured on 61 Cygni by Bessel in 1838
proves that the Earth moves about the Sun: answers objection of ancients to heliocentric hypothesis
stars were further away than any one expected
The nearest star (Alpha Centauri) is 1.3 pc (4.3 ly) away. At 65 MPH, it would take 45 million years to drive there!
Pioneer 10, travelling at 28,000 MPH, will reach vicinity of Aldebaran (68 ly) in 2 million years.

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