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Determining an observer’s latitude and longitude: A primer

Determining an observer’s latitude and longitude: A primer. Longitude. Iowa City 91.5 W. Longitude lines At equator: 360 o = 2 R e  1 o = 111 km (~69 miles) At latitude : 1 o = 111 km · cos( ) ~ 83 km (~51 miles) at Iowa City ( = 41.5 o) Note:

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Determining an observer’s latitude and longitude: A primer

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  1. Determining an observer’s latitude and longitude: A primer

  2. Longitude Iowa City 91.5 W • Longitude lines • At equator: 360o = 2Re  1o = 111 km (~69 miles) • At latitude : 1o = 111 km· cos() ~ 83 km (~51 miles) at Iowa City ( = 41.5o) • Note: • A statute mile (‘mile’) is 1.61 km or 5,280’ • A nautical mile is distance subtended by 1 arcminute in latitude (=1’ longitude at equator), and is 6076’ (1.15 statute miles)

  3. Latitude Iowa City (41.5o N)

  4. Solar declination vs day of year Mar 21 Sep 21

  5. Determining latitude using solar zenith angle, declination Zenith ZA Sun sun Latitude Horizon Latitude = ZA + sun

  6. Determining latitude using a gnomon and noon transit of the Sun Gnomon (Greek ‘one who knows’) Example: At solar transit (~noon) on Sep 1 an observer measures solar zenith angle of 71.9o What is the observer’s latitude? El = 71.9o , soZA = 19.1o sun = 4.2o [Sep 1, from AA or equation]  = sun + ZA = 23.3o N

  7. Determining longitude from UT at solar transit Example: Observe solar transit at 18:23:30 UT on Sept 18. What is observer’s longitude? From AA (Section C) , on Sept 18, teph = 11:54:18 UT, so:

  8. Latitude: same as Sun, only easier- declination does not vary with day of year (but must take into account precession for accurate measurements Longitude: Analogous to the Solar case, we obtain longitude by reference to Greenwich, in this case, the local sidereal time at Greenwich The ‘Greenwich sidereal time’ is the local sidereal time at Greenwich, which can be determined by looking up (in the AA) the GST at midnight for the observing date (GST0, table B) and adding the UT1.0027 (to account for different rates of sidereal vs solar clocks). Example: On June 1, 2007 an observer sees Aldebaran transit at elevation 78.2o from the southern horizon at 4:23:20 UT. Where is the observer? Latitude, longitude using stars

  9. Position from stellar transit: Example

  10. 4 Kings: Four bright stars spaced near the celestial equator (so they can be seen on both N nd S hemispheres) Aldebaran (Taurus, winter evening) Fomalhaut (Pisces, fall evening Antares (Scorpio, summer evening) Regulus (Leo, spring evening) What favorite stars do mariners use?

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