A Warm Up Exercise. Mapping the Earth and Sky and the Motions of the Stars. A Warm Up Exercise. A Warm Up Exercise. A Warm Up Exercise

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1 Mapping the Earth and Sky and the Motions of the Stars A person with a mass of 60 kg goes to the Moon. There she will have a mass of a) othing b) 10 kg c) 360 kg d) 60 kg e) 123 kg A person with a mass of 60 kg goes to the Moon. There she will have a mass of a) othing b) 10 kg c) 360 kg d) 60 kg e) 123 kg Gravity on the Moon is 1/6 that of Earth, so you would weigh 1/6 of your weight on Earth Comet C and comet D are the same distance from the Earth. If Comet C is 1 million km long, comet D is 2 million km long, and comet D subtends an angle of 6 degrees from Earth, then a) Comet C subtends an angle of 12 degrees b) Comet C subtends an angle of 2 degrees c) Comet C subtends an angle of 3 degrees d) Comet C subtends an angle of 6 degrees e) Comet C subtends an angle of 5 degrees Comet C and comet D are the same distance from the Earth. If Comet C is 1 million km long, comet D is 2 million km long, and comet D subtends an angle of 6 degrees from Earth, then a) Comet C subtends an angle of 12 degrees b) Comet C subtends an angle of 2 degrees c) Comet C subtends an angle of 3 degrees d) Comet C subtends an angle of 6 degrees e) Comet C subtends an angle of 5 degrees Key Ideas From Last Time Metric Units The difference between mass and weight The relationship between distance, size and angle angles are proportional to the ratio size/distance 1

2 Key Ideas: The Static Sky -- Constellations Terrestrial Coordinates: Longitude & Latitude Local Horizon & Zenith Celestial Sphere: Celestial Poles & Equator Declination Motions of the Stars - Circumpolar Star The Celestial Sphere To describe where you are and how you are moving you need to have a reference frame The stars provide a natural reference frame on the sky even to the naked eye (which can see about 6000 stars) Zodiacs and constellations were invented to help people locate things on the sky divide the sky into constellations and associate the brightest stars with a picture to help remember it. Orion Ursa Major Hevelius (1690) outside looking in Modern inside looking out Munich Astro Archive In fact, the whole sky is divided into 88 constellations Andromeda, Antlia, Apus, Aquarius.Vela, Virgo, Volans and Vulpecula all properly defined. Constellations as Art (Hevelius) The Constellations Are ot Fixed Rick Pogge But the changes are slow because stellar motions are small. Here is an animation of the changes in the Big Dipper from 100,000 BC to 100,000 AD using the known motions of the stars there are a few fast moving ones 2

3 Finding yourself... Age-old questions of geography: 1) here am I? 2) ho am I? 3) here is someplace else? 4) How do I get there from here? 5) How do I avoid driving through Chicago? Ancient maps usually gave locations in terms of distances and directions from a specific place (e.g., Rome or Alexandria). Fine for a flat earth approximation ot so good on a sphere Angular Coordinates on Spheres Since the Earth s surface is approximately spherical, we use a grid of arcs rather than a rectangular grid. System invented by Claudius Ptolemy (c 140AD), the Father of Modern Geography Ptolemy introduced the minute and second of arc, updating the Babylonian system of using fractions of 60 for subdividing the degree. Positions on the Earth Can be defined by Latitude = how many degrees orth or South of the Equator Longitude = how many degrees est of the prime meridian Columbus just orth of Library, close to the sundial Longitude 83 degrees 00 arcmin 54 arcseconds Latitude 40 degrees 00 arcmin 00 arcsec Prime Meridian? hile the equator (latitude=0 o ) and poles (latitudes= 90 o ) provide a natural way to define latitude, there is no natural way to define longitude you just have to start counting it from somewhere. Longitude=0 o is defined to be the meridian passing through the Greenwich Royal Observatory in England. orth Pole 40º orth Latitude Prime Meridian 40 th Parallel Equator 83º est Longitude Columbus, Ohio: 83º, 40º 3

4 Longitude and Latitude on Earth The circumference of the Earth is m so 1 degree =( m)/ km 1 arcmin =( m)/360/60 2 km (nautical mile) 1 arcsec =( m)/360/60/60 30 m Lost & Found Ptolemy s system was forgotten in Europe after the collapse of the Roman Empire: Flat Earth maps through the middle ages. Maps centered on Jerusalem. Ptolemy was rediscovered, with the Spherical Earth, about 1300: Prime Meridian is Greenwich Psalter Map Ptolemy s Map (1348 version) Features a flat earth centered on Jerusalem (from a medieval book of Psalms, c AD, in the British Museum); To Orient a map. Positions on the Sky Use the Same Idea as Latitude and Longitude Latitude = Declination = angle up or down from celestial equator Longitude = Right Ascension = angle from celestial meridian 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. adir: Point opposite the Zenith, below you. Cardinal Points: orth, South, East & est. 4

5 The Local Sky Zenith S E Horizon avigation - Latitude Easiest to determine as the angle between the horizon and the pole star (i.e. something exactly at the orth Celestial Pole) in practice you can use anything with a known declination (celestial latitude) avigation Longitude Longitude is much harder because you must separate position from time suppose you know that a star lies on the prime meridian of celestial longitude and you note when it passes your local meridian. But knowing your celestial longitude is not enough to get your longitude on Earth because the Earth rotates you need to know your celestial longitude and the time. Simplest is to carry a clock that keeps time at the prime meridian in Greenwich when the clock says noon, it is noon in Greenwich. ow measure the time of your local noon on the Greenwich clock if it is 5:36pm, then you are at the longitude of Columbus but you need a good clock because an error of 1 second of time corresponds to 15 seconds of arc (24 hours versus 360 degrees) or 0.5 km on the Equator. H4 clock (1761) The Longitude Prize In 1714 the British government offered a 20,000 pound (about $2 million today) prize for a method to measure longitude with a precision of 0.5 o (=2 minutes of time=55km on the Equator). The board administering the prize was absolutely convinced that the solution lay in astronomy. An English clockmaker John Harrison was the first to suceed, with the H4 clock (he started with the H1 in 1730), which in a 60 day voyage to Jamaica was off by only 5 seconds. On a second trial it was of by 40 seconds, but that was still three times better than required. The board refused to pay out until overruled by King George III and Parliament. The first copy of the H4 was taken by Captain Cook on his second voyage to the Pacific in the three year voyage it was never off by more than 8 seconds of time, or about 3.5km. You can do it all with astronomy it involves lunars which use tables of the position of the moon relative to stars to work out (essentially) the time. The Modern ay -- GPS 31 satellites with atomic clocks, each broadcasting an encoded time and satellite position. Receiver computes distance from each satellite based on the satellite position and the time it took the signal to go from the satellite to the receiver limits your position to the surface of a sphere surrounding each satellite. Your position is where all the sphere s overlap in theory you want 4 satellites (to also correct your receiver s clock) but can use three if you know you are on the Earth s surface. 1 sphere 2 circle 3 point 5

6 The Daily Motion of the Stars Due to the rotation of the Earth hat you see (or can see) is controlled by your latitude Daily Motions Objects in the sky appear to rise in the East and set in the est each day. This apparent daily motion is a reflection of the Earth s rotation about its axis. Earth rotates once a day (24 hours) The sense of rotation is Eastward Facing orth, rotation is towards the Right. A very simple experiment to show the Earth rotates The Foucault Pendulum (1856) The plane in which a pendulum swings stays fixed, so you can see the Earth rotating relative to this fixed plane a common feature in science museums (including COSI), but invented an amazingly long time after the experiment became possible! Franklin Institute Apparent Paths of Stars The Apparent Paths of objects are parallel to the Celestial Equator. Their orientation depends on your latitude: At Equator: perpendicular to the horizon At Poles: parallel to the horizon Mid-Latitudes: Tilted by (90º Latitude) In Columbus (40º ): Apparent paths are tilted 50º from the horizon. At Latitude = 30º the paths are tilted by 90º 30º=60º At Latitude = 0º the paths are tilted by 90º 90º=0º 6

7 S Z E Equator S CP Z CP CP Z orth Pole Circumpolar Stars Any star closer than your latitude to your visible celestial pole (north or south) will always be above your horizon. These are the Circumpolar Stars Ursa Major, Ursa Minor, & Draco are circumpolar constellations from Columbus The opposite pole s circumpolar stars for the same latitude never rise above your horizon. Ursa Major never rises for latitudes below 40º S 40º Latitude Above Horizon for 12 h Above Horizon for < 12 h S ever Rises Above Horizon for > 12 h E Zenith CP ever Sets CEq Summary of Daily Motions: Daily Motions of celestial objects reflect the Earth s daily rotation about its axis: Celestial objects to appear to rise in the East and set in the est. Their paths are parallel to the Celestial Equator. The inclinations of these paths relative to the horizon depends on the observer s latitude. Circumpolar objects are those always above or below the local horizon. Celestial Coordinates Latitude = Declination = angle up or down from celestial equator Longitude = Right Ascension = angle from celestial meridian But where do you count right ascension from? Clearly, Greenwich England is a bad idea since the earth spins.. You reference it to the stars it is defined to be the meridian of the Vernal Equinox (it s in the constellation Pisces) The Vernal what? 7