Astronomy 161
Introduction to Solar System Astronomy
Prof. Paul Martini

Lecture 2: Mapping the Earth and Sky

Key Ideas

Location? Location? Location?

Fundamental questions of geography:: 1. Where am I?; 2. Where is somewhere else?; 3. How do I get there?
Ancient maps gave distances and directions from a specific place (e.g. Rome): Fine for a flat Earth approximation; Not as good on a sphere

Ptolemy: The Geographer

Greek astronomer and geographer
Lived c. 100-150 AD in Alexandria, Egypt
Knew the world was a sphere and that the 'known world' was only a quarter of the globe
Devised projection map to account for curvature

Dividing the Earth

Latitude and Longitude

Lost and Found

The system of Latitude and Longitude was introduced by Claudius Ptolemy (circa 140 AD)
It was forgotten in Europe after the collapse of the Roman Empire:: Flat Earth maps through the Middle Ages.; ''T-O'' maps centered on Jerusalem
Ptolemy was rediscovered, with the Spherical Earth, about 1300 AD:: The Prime Meridian goes through Greenwich; In Ptolemy's time it went through the Fortunate Isles (Canaries), which were the western limit of the known world.

The Prime Meridian

The International Meridian Conference of 1885 established:: An initial (or Prime) meridian shall be established at Greenwich; The Universal day shall be the mean solar day; The mean solar day shall begin at midnight, both at sea and on land; 22-1 vote in favor; (San Domingo opposed, France, Brazil abstain)

Celestial Sphere

The stars are projected onto a Celestial Sphere centered on the Earth
Celestial Equator: Projection of Earth's Equator onto the sky
Celestial Poles: Intersection of Earth's Poles with the sky
Celestial Meridian:: Great Circle from the NCP to the SCP through a given object
Declination: Angle along Celestial Meridian from Celestial Equator to the object; Celestial Equivalent of Latitude; Measured in degrees
Celestial Longitude: Not simply the projection of the Prime Meridian due to the rotation of the Earth
Right Ascension: We'll discuss the celestial equivalent of longitude in a future lecture

The Local Sky

Standing on the Earth, we can only see half of the sky at any instant:: One half stretches overhead to the Horizon; Other half is below the Horizon
Zenith: Point directly overhead.
Nadir: Point opposite the Zenith, below you
Cardinal Points: North, South, East, and West
Meridian: Runs North-South through Zenith

The Local Sky (cont'd)

What part of the Celestial Sphere you can see depends on: Where you are on the Earth (Latitude and Longitude); What time it is (date and time)
Effect: objects in the sky: Rise above the Eastern Horizon and; Set below the Western Horizon
as the Earth rotates.

Celestial Navigation

The Angle between the North Star and Horizon (when pointing North) is your Latitude
If you can measure the altitude of Polaris, you can measure your Latitude

Longitude

Logitude is substantially more difficult to measure than latitude because the Earth rotates
Logitude determination requires knowledge of time, auch as the difference in local solar noon at two locations.
In 1714, the British government offered 20,000 pounds (equivalent to over ten million today) for a solution to the "Longitude Problem" that would:: Determine longitude to within 0.5 degrees (2 min of time or about 35 miles); Work at sea; Survive a trip between Great Britain and the West Indies
The prize was finally won by John Harrison (1693-1776)

Angles and Distance

If the size of an object is known, its distance can be measured by measuring the angle it subtends
If the angle is small:: d = 57.3/angle AU where 'angle' is measured in degrees; d = 206265/angle AU where 'angle' is measured in arcseconds

Very Small Angles

A complete circle is divided into 360 degrees
Degrees are divided into arcminutes ('):: 1 degree divided into 60 minutes of arc; minute comes from pars minuta prima (first small part); 1 minute = 1/60th of a degree
Arcminutes are divided into arcseconds (''):: 1 minute divided into 60 seconds of arc; second comes from parte minutae secundae (second small part); 1 second = 1/3600th of a degree (very small!)

Subdividing the Degree

Question: Why 360? 60?
Answer: The Babylonians: 360 is close to 365, the number of days in a year; 360 is dividible by 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, and 180 without using fractions; 60 is divisible by 2, 3, 4, 5, 6,10, 12, 15, 20, and 30 without using fractions; (100 is only divisible by 2, 4, 5, 10, 20, 25, 50)
The Babylonians subdivided the degree as fractions of 60, for example:: 7 14/60 degrees
Claudius Ptolemy introduced the modern notation:: 7 degrees 14' 00''

The Parsec

A parsec is defined as the distance at which 1 AU will subtend 1 arcsecond.
The angular shift of stars over the course of the year is used to measure the distance of nearby stars
Proxima Centauri, at 1.26 pc, moves 1/1.26 or 0.8 arcseconds when the Earth moves 1 AU (6 months)

See A Note about Graphics to learn why some of the graphics shown in the lectures are not reproduced with these notes.