Measuring the Sky

How Geometry Makes Astronomy Happen

Overview

• How it started – Eratosthenes and Hipparchus measure the world
• The size of the earth
• The distance to the moon and sun
• How far are the stars? Parallax
• Bringing it forward: the language of astronomy
• Horizon, Zenith, Altitude, Azimuth
• The moving sky
• Mapping the stars
• Triangles and telescopes – the ancient art of star hopping

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Eratosthenes Measures the Earth

• 276 BC-194 BC
• Born in Cyrene
• Worked in Alexandria
• Apparently made entirely of marble, as were most of the ancient Greeks

A little geography, a little geometry…

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Corresponding Angles are Equal

Gamma ~7 degrees, or 1/50 of a circle

5,000 stadia times 50 =250,000 stadia

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1 stadia = 509-525 feet

250,000 stadia = 24,100-24,857 miles

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Hipparchus measures the Moon…

• c. 190BC- c.120 BC
• Founder of Trigonometry (loved him some triangles)
• Considered by some to be the greatest ancient astronomer
• Compiled the star catalog that is still the basis for what we use today (much amended and corrected, of course)

Parallax and pitfalls….

• Hipparchus used similar methodology to Aristarchus, a Greek astronomer several centuries earlier
• Estimated the size and distance of the moon based on:
• Time it took the moon to move through earth’s shadow during an eclipse
• Parallax of the moon during a solar eclipse
• His estimates for the moon were relatively accurate, considering the limitations of his technology
• He was way off on the Sun’s distance. Why?

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What is parallax?

Apparent position changes with viewpoint

Used to find distances to stars

Accuracy diminishes with distance…

Stargazing tonight: the language of astronomy

• How do we talk about the sky?
• Some basic terms and concepts

Horizon

Meridian

Altitude and azimuth

• Altitude– how high something is above the horizon
• Azimuth – where it is along the horizon
• How do we measure altitude and azimuth?

Meet your new measuring device – your hand!

• Hold your hand at arms length
• Accurate for everyone
• Now you can measure the sky!

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Some useful measures…

How it all moves…

Mapping the stars

• Alt-az is very good for pointing out something that is not moving very fast
• Less good for referencing things that do move
• The sky moves
• We use a different system, similar to latitude and longitude, to map the stars

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Celestial Coordinates

• Right Ascension is similar to longitude. All stars on the same RA line cross your meridian at the same time. Measured in hours and minutes (and seconds)
• Declination is like latitude – measures degrees north or south of the celestial equator

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A heavenly address…

• RA 13h 00m Dec 10 deg 30 sec?
• Vindemiatrix
• RA 15 h 59m 30 sec Dec 25 55 sec?
• Tau Corona Borealis (not on map –what’s it near?)

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• What are coordinates of alpha Scorpii – Antares?
• RA 16h30m Dec -26
• Arcturus in Bootes?
• RA 14h 15m Dec 19h 30m
• These coordinates are how modern “go to” scopes find things in the sky

Triangles and Telescopes – the ancient art of star hopping

Star hopping – let triangles point your way

• M80 in Scorpius

First, 7x50 binoculars…

Hop to next star and find a route…

Next, the telescope eyepiece…

Next, telescope. Eyepiece view…

A triangle points the way…

Questions?