ASTR1102 002 Potentially useful facts and mathematical relations A A star at a distance of 1 parsec 1 pc 3 26 light years exhibits a parallax of 1 arcsecond That is p 1 arcsec d 1 pc More generally if p is measured in arcseconds then the distance d in parsecs can be calculated using the formula d 1 p B A star s apparent brightness varies as the inverse square of its distance from us That is b b0 d d0 2 d0 d 2 C Each difference of 5 magnitudes m or M corresponds to a factor of 100 in brightness For example m2 m1 5 b1 b2 100 m2 m1 5 b1 b2 1 100 0 01 b1 b2 100 100 10 000 104 m2 m1 10 D The distance to a star can be determined straightforwardly from the star s tabulated distance modulus m M Examples m M 0 m M 5 m M 10 m M 5 d 10 pc d 100 pc d 1000 pc d 1 pc The more general formula that is used to relate the value of m M to distance is see Box 17 3 in the textbook m M 5 log d 5 1 Practice Questions for Exam 1 1 A star that is closer to us than 1 pc exhibits a stellar parallax that is larger or smaller than 1 arcsec ANS 2 Star Q is twice as far away from us as star R Which of the following statements is true a The parallax of star Q is twice as large as the parallax of star R b The parallax of star R is twice as large as the parallax of star Q c The parallax of star Q is 4 times as large as the parallax of star R d The parallax of star R is 4 times as large as the parallax of star Q ANS 3 star A is brighter You are told that mA mB 0 Which star A or B appears to be brighter in the night sky ANS 8 star B is brighter You are told that mA mB 8 Which star A or B appears to be brighter in the night sky ANS 7 star R You are told that mA mB 3 Which star A or B appears to be brighter in the night sky ANS 6 100 pc Star Q has an apparent magnitude of 4 0 and star R has an apparent magnitude of 1 0 Which star appears to be the brighter in the night sky ANS 5 b A star with a measured parallax of 0 01 arcsec is at a distance of pc from us Fill in the blank ANS 4 Larger stars are the same brightness You are told that mA mB is a negative number Which star A or B appears to be brighter in the night sky ANS star A is brighter 2 9 You notice that one particular star in a star catalog has an absolute magnitude M that is larger in value than its apparent magnitude m Is this star closer to us than 10 pc or farther from us than 10 pc ANS 10 You are told that a particular star exhibits a distance modulus m M of zero How far away from us is this star ANS 11 61 Cygni A Which of the 6 stars listed in Table 1 is closest to us ANS 18 Rigel Which of the 6 stars listed in Table 1 is intrinsically the faintest ANS 17 Sirius A Which of the 6 stars listed in Table 1 is intrinsically the brightest ANS 16 stellar parallax Which of the 6 stars listed in Table 1 appears to be the brightest in the night sky ANS 15 m M 5 The most direct way for an astronomer to determine the distance to an individual star is to measure its Fill in the blank ANS 14 d 100 pc A star with a measured stellar parallax p 0 01 arcsec has a distance modulus m M ANS 13 d 10 pc You are told that a particular star exhibits a distance modulus m M 5 How far away from us is this star ANS 12 Closer than 10 pc Alpha Centauri A Which of the 6 stars listed in Table 1 is farthest from us ANS Rigel 3 19 Which of the 6 stars listed in Table 1 has an intrinsic brightness that is most similar to the intrinsic brightness of the Sun ANS Page 441 of the textbook points out that the Sun has an absolute magnitude M 4 8 hence Alpha Centauri A has an intrinsic brightness most similar to the Sun Table 1 Star Name Sirius A Alpha Centauri A 61 Cygni A Rigel Regulus Vega 20 Apparent magnitude m 1 43 0 01 5 21 0 12 1 35 0 03 Absolute magnitude M 1 46 4 36 7 49 6 75 0 53 0 58 Dopper shift or radial velocity Star A and star B have exactly the same measured proper motions 1 arcsec year but star A exhibits a parallax of 0 25 arcesecs and star B has a parallax of 0 15 arcsec yr Which star is moving through space with the faster speed a Star A is moving faster than star B b Star B is moving faster than star A c The stars are moving through space at the same speed d None of the above Briefly explain ANS 22 Proper Motion arcsec year 1 34 3 71 5 28 0 002 0 25 0 35 The most direct way for an astronomer to determine the speed at which a star is moving toward or away from us is to measure the star s Fill in the blank ANS 21 Parallax p arcsec 0 380 0 746 0 286 0 00422 0 0420 0 129 b How many years will it take the star Regulus to move to a coordinate location on the sky that is 1 degree away from its present coordinate location ANS 0 25 arcsec year hence 4 it will move 1 arcsec in 4 years 1 arcmin in 4 x 60 240 years and 1 degree in 60 x 240 14 400 years 4 23 A hurricane that is in the middle of the Gulf of Mexico west longitude 90 degrees latitude 24 degrees is observed to be moving due north headed for New Orleans west longitude 90 degrees latitude 30 degrees If the hurricane forecasters report that the eye of the hurricane will hit New Orleans in 48 hours what is the observed proper motion of the hurricane ANS 24 What astronomer s technique does a police officer usually use in order to measure whether or not you are speeding a The officer measures your car s proper motion b The officer relies on a Doppler shift measurement c The officer measures the apparent brightness of your headlights d The officer measures the color of your car ANS 25 6 degrees 48 hours NOTE This is the same as 3 degrees day 1096 degrees year or approximately 4 million arcsec …