Retrograde Motion, Triangulation & Conclusion Part I

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?)

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

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

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.

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

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

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.

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

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

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

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.

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”

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