Observing Stars and Planets - Can We Observe x Tonight

Can We Observe x Tonight? This is an important question to be able to answer, this being an observing subject and all. The answer to this question is “yes” only if the answer to the following 4 questions is “yes”: 1.Is the weather cooperating? 2.Is x bright enough, given our observing equipment? 3.Is the sky dark enough? 4.Is x high enough above our horizon? This handout addresses the answering of questions 2, 3, and 4, and explains how to use information published in the Astronomical Almanac to decide whether to go for a specific object at any given time. As for question 1, that's a different class... (12.310) Contents 1 Brightness Scale........................................................................................................... 2 1.1 Effects on apparent brightness ............................................................................... 3 2 Coordinate Systems...................................................................................................... 4 2.1 Terrestrial coordinates ........................................................................................... 4 2.2 Celestial coordinates.............................................................................................. 5 2.3 Observer-based coordinates................................................................................... 6 3 Time Scales.................................................................................................................. 6 3.1 Solar times ............................................................................................................ 6 3.2 Sidereal times........................................................................................................ 6 4 Sun/Moon Rise/Set tables ............................................................................................ 7 5 Other useful items in the Astronomical Almanac.......................................................... 8 1 1 Brightness Scale The magnitude system refers to the numeric scale used by astronomers to quantify object brightness. Its rather baroque character can be traced to its origins over 2000 years ago, when the Greek scholar Hipparchus first began visually classifying stars into six brightness categories, with the brightest stars called "stars of the first magnitude", slightly fainter ones "stars of the second magnitude", and so on. When 19th century astronomers sat down to come up with some sort of mathematical expression corresponding to Hipparchus' original six magnitudes, it was discovered that the brightness of some of the stars he'd assigned magnitude 1 were actually too bright to be so classed based on the rest of his system; these brightest stars now carry magnitudes of 0 and -1. Oops. But, let's press on, shall we? energy Call the intensity of light source n In, measured in area ◊time . The difference in magnitude between objects with respective intensities I1 and I2 is then defined as Dm = m2 - m1 ∫ -2.5 log10 I2 I1 (1) This definition can be rearranged to show the admittedly non-intuitive relationship between the objects' intensities in terms of magnitudes: -0.4 Dm = log I2 I ; 10 -0.4 Dm = 2 ; I2 = I1 ◊ 10 -0.4 Dm I1 I1 (2) Happily, for most of our purposes here in the seminar we won't need to mess around with Equation 1 up there; a few tabulated values should prove sufficient: Dm 0 1 2 2.5 3 4 5 I2/I1 1.0 ª2.5 ª6.3 10 ª16 ª40 100 Object Magnitude Sun Full Moon Venus (at brightest) Jupiter Sirius (a Cma) -26.8 -13.6 -4.4 -2 -1.4 Vega (a Lyr) Uranus quasar faintest object detected (Earth-based) (ª_glow of cigar on Moon seen from Earth) 0.0 +6 (naked eye limit) +13 +29 2 1.1 Effects on apparent brightness 1.Extinction: Loss of light as it passes through the atmosphere. Normal extinction on a clear night is about 0.2 mag. at the zenith and increases quickly as you start looking at lower altitudes. 2.Telescope: How much does it help us? It collects an amount of light proportional to the AREA of the objective mirror, as shown in Figure 2. For dark adapted pupil For 8” LX200 telescope How many magnitudes fainter should we be able to see (theoretically) with the LX200, under IDEAL conditions (clean and otherwise perfect optics, ...)? I2 Atelescope = I1 Aeye (3) 3. Effect of distance on apparent brightness is known as the “inverse square law.” The changing brightness of Mars is due mostly due to its changing distance as it orbits the Sun. This also contributes to changes in brightness of Venus (along with phase, the amount of the disk that we see illuminated by the Sun). 3 Here's how the change, in magnitudes, depends on distance --- if an object with distance R away from an observer appears to be magnitude M, then from a different distance r the same object would appear to be magnitude m according to m - M = Dm = -2.5 log I (r ) I ( R) Ê I ( R) ◊ R 2 r 2 ˆ = -2.5 logÁ ˜ Ë I ( R) ¯ (4) Ê R2 ˆ = -2.5 logÁ 2 ˜ Ër ¯ = -5 log R r This last form of the equation is commonly known as the distance modulus. 2 Coordinate Systems 2.1 Terrestrial coordinates f): + north / - south of the equator (range: -90°