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Astronomy without a Telescope. Angular Measurements. There are 360 degrees in a full circle and 90 degrees in a right angle Each degree is divided into 60 minutes of arc A quarter viewed face-on from across the length of a football field is about 1 arc minute across.
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Angular Measurements • There are 360 degrees in a full circle and 90 degrees in a right angle • Each degree is divided into 60 minutes of arc • A quarter viewed face-on from across the length of a football field is about 1 arc minute across. • Each minute of arc is divided into 60 seconds of arc • The ball in the tip of a ballpoint pen viewed from across the length of a football field is about 1 arc second across. • The Sun and Moon are both about 0.5 degrees. • Bowl of the Big Dipper is about 30 degrees from the NCP • Any object ``half-way up'' in the sky is about 45 degrees above the horizon
This is the preferred coordinate system (Equatorial Coordinates) to pinpoint objects on the celestial sphere. Unlike the horizontal coordinate system, equatorial coordinates are independent of the observer's location and the time of the observation. This means that only one set of coordinates is required for each object, and that these same coordinates can be used by observers in different locations and at different times. The equatorial coordinate system is basically the projection of the latitude and longitude coordinate system we use here on Earth, onto the celestial sphere. By direct analogy, lines of latitude become lines of declination (Dec; measured in degrees, arcminutes and arcseconds) and indicate how far north or south of the celestialequator (defined by projecting the Earth's equator onto the celestial sphere) the object lies. Lines of longitude have their equivalent in lines of right ascension (RA), but whereas longitude is measured in degrees, minutes and seconds east the Greenwich meridian, RA is measured in hours, minutes and seconds east from where the celestialequator intersects the ecliptic (the vernal equinox).
At first glance, this system of uniquely positioning an object through two coordinates appears easy to implement and maintain. However, the equatorial coordinate system is tied to the orientation of the Earth in space, and this changes over a period of 26,000 years due to the precession of the Earth's axis. We therefore need to append an additional piece of information to our coordinates - the epoch. For example, the Einstein Cross (2237+0305) was located at RA = 22h 37m, Dec = +03o05' using epoch B1950.0. However, in epoch J2000.0 coordinates, this object is at RA = 22h 37m, Dec = +03o 21'. The object itself has not moved - just the coordinate system. The equatorial coordinate system is alternatively known as the 'RA/Dec coordinate system' after the common abbreviations of the two components involved.
Time: UTC (Zulu Time, GMT) Sidereal Time or “Star Time” The solar day is slightly longer than the sidereal day. The solar day is 24 hours and the sidereal day is 23 hrs and 56 minutes. See page 177 ESSAY TWO for a full explanation. We will return to this later.
You can scale sky distances with your hand. For most people a fully spread hand at arm’s length covers about 20o of sky or about the length of the Big Dipper from the tip of the handle to the bowl. Finger widths alone give just a few degrees.
Measuring the Diameter of Astronomical Objects To find an astronmical’s body true diameter from its angular diameter if we know its distance. The angular size of a distant object changes inversely with the objects distance.
The scaling of distances with your hand makes it easy to point out stars to other people.
Azimuth Two ways of measuring the position of stars. Topo-centric Coordinates (right) and Celestial Coordinates (left). What are advantages and disadvantages of both. As a star rises and moves across the sky, which of the following change? (a) its right ascension (b) Its declination (c) its azimuth (d) both (a) and (b) (e) none of the above.
Note that A is expressed in degrees and that L and D are in the same units.
Problem Example The great galaxy in Andromeda has an angular diameter along its long axis of about 5°. Its distance is about 2.2 million light-years. What is its linear diameter? L = 0.192 x 106 Light Years or L = 1.92 x 105 Light Years
A shell of gas blown out of a star has an angular diameter of 0.1° and a linear diameter of 1 light-years. How far away is it? D = 572.96 ~ 573 ly
Eratosthenes measured the shadow length of a stick set vertically in the ground in the town of Alexandria on the summer solstice at noon, converting the shadow length to an angle of solar light incidence, and using the distance to Syene, a town where no shadow is cast at noon on the summer solstice Review of Eratosthenes Problem as a teaching aid to the Myrmidon problem
How you can do much of backyard astronomy by deductive reasoning. This sketch shows how Eratosthenes (Pronunciation: \-ˌer-ə-ˈtäs-thə-ˌnēz\)of Cyrene (276 BC - 194 BC) used the length of a shadow at two different locations to determine the Earth’s size. You need to collaborate with someone at least several hundred miles north or south of you. Set up a vertical stick and a piece of paper beside the stick. Record the shadow at two different locations. You must know the straight line distance between the two locations. Measure the angles A and B at the top of the triangles. Suppose the earth’s circumference is 40,007.86 km (meridional) and the radius is 6367 km. What would be the angle A – B for B at the equator and A 250 km due North?
The Myrmidon Size Problem Suppose you were an alien living on the fictitious warlike planet Myrmidon and you wanted to measure its size. The Sun is shining directly down a missile silo 1000 miles to your south, while at your location, the Sun is 36° from straight overhead. What is the circumference of Myrmidon? What is its radius? You are here a Angle a is 36o C = 10,000 miles Missile silo is here a 1000 miles south of you a 2R= 10000 R = 10000/ 2 R = 1592 miles Myrmidon
Figure 1.26 The Geocentric Theory of Ptolemy, Aristotle et al
Astronomy in the Renaissance • However, problems remained with the geocentric theory: • Could not predict planet positions any more accurately than the model of Ptolemy • Could not explain lack of parallax motion of stars • Conflicted with Aristotelian “common sense” • Problems were solved by Nicolaus Copernicus with his heliocentric theory. He placed the sun at the center (of our solar system) Nicolaus Copernicus (19 February 1473 – 24 May 1543)
The puzzle of retrograde motion was one of the reasons that the geocentric theory was not accepted by Nicholaus Copernicus but was easily explained by heliocentric theory Copernican Theory was also accepted by Galileo Galilei (born 15 February 1564– died 8 January 1642) Both Galileo and Copernicus had difficulty with the Copernican theory because of religious views
The moon returns to the same position with respect to the background stars every 27.323 days. This is its sidereal period.
Astronomy in the Renaissance • Tycho Brahe (1546-1601) • Designed and built instruments of far greater accuracy than any yet devised • Made meticulous measurements of the planets
Astronomy in the Renaissance • Tycho Brahe (1546-1601) • Made observations (supernova and comet) that suggested that the heavens were both changeable and more complex than previously believed • Proposed compromise geocentric model, as he observed no parallax motion!
Astronomy in the Renaissance • Johannes Kepler (1571-1630) • Upon Tycho’s death, his data passed to Kepler, his young assistant • Using the very precise Mars data, Kepler showed the orbit to be an ellipse
Kepler’s 1st Law • Planets move in elliptical orbits with the Sun at one focus of the ellipse
Kepler’s 2nd Law • The orbital speed of a planet varies so that a line joining the Sun and the planet will sweep out equal areas in equal time intervals • The closer a planet is to the Sun, the faster it moves
Kepler’s 3rd Law • The amount of time a planet takes to orbit the Sun is related to its orbit’s size • The square of the period, P, is proportional to the cube of the semimajor axis, a
Kepler’s 3rd Law • This law implies that a planet with a larger average distance from the Sun, which is the semimajor axis distance, will take longer to circle the Sun • Third law hints at the nature of the force holding the planets in orbit
Kepler’s 3rd Law • Third law can be used to determine the semimajor axis, a, if the period, P, is known, a measurement that is not difficult to make
Some Tips in General Observing • The longer you stay out at night the more sensitive your eyes will become (dark adaptation) • The pupils open wider. The pubils have a normal diameter of 2 mm but in total darkness they may expand to 7 or 8 millimeters • Chemical changes in the retina make it about 1 million times more sensitive to light than in full daylight • In addition to becoming more sensitive to light your eye also changes sensitivity to color (Purkinje effect). It becomes more sensitive to the blue. (this is why blue lights are used in insect attractors) • It is easier to see faint objects if you look to the side of them (averted vision). The center of your field of view is densely packed with receptors that allow you to see fine detail.
Tip of the Day: (1) How sunrise to sunset is defined. Sunrise is time from just when the top of the sun clears the horizon to sunset when the last bit of sun disappears. (2) Astronomy Magazine Sept. 2002 issue defines the faintest naked eye star at 6.5 apparent magnitude. “Apparent Magnitude”was defined by Hipparachus in 150 BC. He devised a magnitude scale based on: Magnitude Constellation Star 1 (Orion) Betelgeuse 2 Big Dipper various 6 stars just barely seen However, he underestimated the magnitudes. Therefore, many very bright stars today have negative magnitudes. Magnitude Difference is based on the idea that the difference between the magnitude of a first magnitude star to a 6th magnitude star is a factor of 100. Thus a 1st mag star is 100 times brighter than a 6th mag star. This represents a range of 5 so that 2.512 = the fifth root of 100. Thus the table hierarchy is the following. Absolute Magnitude is defined as how bright a star would appear if it were of certain apparent magnitude but only 10 parsecs distance. Magnitude Difference of 1 is 2.512:1, 2 is 2.5122:1 or 6.31:1, 3 is 2.5123 = 15.85:1 etc.
