Determining an observer’s latitude and longitude: A primer
10
Determining an observer’s latitude and longitude: A primer
description
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: - PowerPoint PPT Presentation
Transcript of Determining an observer’s latitude and longitude: A primer
Determining an observer’s latitude and longitude: A primer
Longitude
Longitude lines • At equator: 360o = 2Re 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)
Iowa City91.5 W
Latitude
Iowa City (41.5o N)
Solar declination vs day of year
Mar 21 Sep 21
Determining latitude using solar zenith angle, declination
ZA
Zenith
Sun
Horizon
Latitude
sun
Latitude = ZA + sun Latitude = ZA + sun
Determining latitude using a gnomon and noon transit of the Sun
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 , so ZA = 19.1o
sun = 4.2o [Sep 1, from AA or equation]
= sun + ZA = 23.3o N
Gnomon (Greek ‘one who knows’)
Determining longitude from UT at solar transit
λ(W ) = tobs _ transit (UT ) − tephemeris _ transit (DOY )
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:
λ =18 : 23 : 30 −11 : 54 :18 = 06 : 29 :12 = 97o18 ' W
Latitude, longitude using stars
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 UT1.0027 (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?
λ =GST −α = GST 0 +UT ⋅1.0027 −α
Position from stellar transit: Example
What favorite stars do mariners use?
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)
