Pointing and Tracking Astrophysical Objects
Frisco Peak Telescope Control Panel
Frisco Peak Telescope
– Pointing and
Tracking Precision less than 10 arcsec
(Angle subtended by a penny at roughly 200 yards)
1 radian=206,264.98 arcsec

The Altitude-Azimuth Coordinate System
•
Coordinate system based on observers local horizon
• Zenith - point directly above the observer
• North - direction to north celestial pole
NCP projected onto the plane tangent to the earth at the observer ’ s location
• h: altitude - angle measured from the horizon to the object along a great circle that passes the object and the zenith
• z: zenith distance - is the angle measured from the zenith to the object z+h=90

•
A: azimuth - is the angle measured along the horizon eastward from north to the great circle used for the measure of the altitude

• Coordinate system based on a projection of the Earth ’ s geographic poles and equator onto the celestial sphere
• Celestial Poles - Points on celestial sphere intersected by line coincident with Earth ’ s rotation axis. North and South.
• Celestial Equator - Projection of Earth ’ s
Equator onto the the celestial sphere.
 
: Declination - The latitudinal angle measured from the celestial equator to the object along a great circle that passes through the object and the celestial poles.
Objects north of the celestial equator have declinations in the range from 0 to +90 degrees. Objects south of the celestial equator have declinations in the range from
0 to -90 degrees.
 
: Right Ascension - The longitudinal angle measures the angle of how far east an object lies from the Vernal Equinox.
 
: Vernal Equinox - Point on celestial equator where the path of the sun crosses the celestial equator.

Meridian
• Meridian - Imaginary line through the Zenith and North Celestial Pole extended along a great circle on the celestial sphere to the northern and southern horizon

Hour Angle and Local Sidereal Time
•
Local Sidereal Time (LST) - The amount of time that has elapsed since the Vernal
Equinox (point) last traversed the local meridian.
• Hour Angle - The hour angle (HA) of an object is equal to the difference between the current local sidereal time (LST) and the right ascension (α) of that object:

•
Due to slow wobble of Earth ’ s rotation axis caused by Earth ’ s non-spherical shape and gravitational interaction with the Sun and planets
•
Precession period is 25,770 years
• Pole will sweep out a circle on the sky with angular diameter of nearly 47 degrees!!!
•
Impacts the values of RA and DEC of objects over time ==> Epochs. The change in values of RA and DEC from their values in the year
2000.0 are given by:
M
=
1.2812323
T
+
0.0003879
T
2 +
0.0000101
T
3
N
=
0.556753
T
-
0.0001185
T
2
T
=
( t
-
2000.0) /100
-
0.0000116
T
3

Even More Astronomical Coordinate Systems…
Other coordinate systems may be more appropriate …
For instance mapping objects in the milky way is best done using galactic coordinates
Conversions between coordinate systems are possible…with a little math!!!

Changes in the Sky
• Coordinates continuously changing in alt-az system for all celestial objects
(except geo-stationary satellites)
• Earth ’ s rotation
• Earth ’ s orbit about Sun
• Proper motion of objects
– The moon
– Planets
– Asteroids
– Comets
– Satellites….
Milky Way From Frisco
Peak. Paul Ricketts


Earth ’ s Rotation
• Earth ’ s rotation is responsible for the “ rapid ” motion of objects through the sky
Mud springs point 2 hour exposure of NCP. Paul Ricketts


Tilt of Earth ’ s Axis

Seasonal Changes
•The Sun ’ s motion across the sky changes over the course of the year. This is due mainly to the tilt of the Earth ’ s rotation axis.
•The maximum angular height above the horizon at a location in the Northern
Hemisphere is maximum on the Summer
Solstice and minimum on the Winter
Solstice. This results in sunlight being spread over a larger area during Winter causing a reduction in heating of the surface of the Earth at Northern latitudes during Winter.
• The values of the Sun ’ s RA and DEC change over the year as shown in the graph.

Earth ’ s Orbit about the Sun
The Ecliptic.The path of the sun through the year in equatorial coordinates.
Due to the Earth ’ s motion about the Sun :
– Line of sight to the sun sweeps through the constellations. The sun apparently moves through the constellations of the zodiac along a path known as the Ecliptic
– The constellations that are visible each night at the same time changes with the season
– A given star will rise approximately 4 minutes earlier each day

The period (sidereal) of earth ’ s revolution about the sun is 365.26 solar days. The earth moves about 1
 around its orbit in
24 hours.
•
Solar day
– Is defined as an average interval of 24 hours between meridian crossings of the Sun.
– The earth actually rotates about its axis by nearly 361
 in one solar day.
•
Sidereal day
– Time between consecutive meridian crossings of a given star.
The earth rotates exactly 360
 w.r.t the background stars in one sidereal day = 23h 56m 4s

•
The curve traced on the sky by the position of the Sun at local noon over the course of the year.
•
The change in altitude
(declination) is the result of the tilt of the earth ’ s rotation axis.
•
The change in hour azimuth
(hour angle) is due mainly to the variation in the length of the solar day resulting from the
Earth ’ s elliptical orbit.
• For more info see.…
• http://www.annalemma.com

Proper Motions
Celestial objects may have their own proper motion…including stars, galaxies…
Radial motion is along the line of sight.
Transverse motion is the component of motion perpendicular to the line of sight to the object.

Measurements of Time
• Gregorian Calendar - Calendars which label months and dates for each year need to account for the fact that Earth ’ s revolution period is not an integer number of days…--> Leap Years, Leap
Seconds,…
• Julian Date - Astronomers typically refer to the times when observations were made in terms of elapsed time since some specified zero time. The zero time that is used is noon on
January 1,4713 BC…JD0.0. The Julian date of J2000.0 is
JD2451545.0. Times other than noon Universal time are specified as a fraction of a day. MJD=JD-2400000.5. MJD begins at midnight instead of noon…

Celestial Sphere and Spherical Trigonometry
Side= arc of great circle
Angle=angle between sides
Law of Sines sin a sin A
= sin b sin B
= sin c sin C
Law of Cosines for sides cos a
= cos b cos c
+ sin b sin c cos A
Law of Cosines for angles cos A
= cos B cos C
+ sin B sin C cos a
Sum of angles of spherical triangle<180 degrees

Celestial Sphere and Spherical Trigonometry
Want to find opening angle
Dq
Given
D and
D
Apply law of sines sin(
D J
) sin(
D a
) sin(
D a
=
)cos( sin[90
-
( d + D d
)] d +D d sin
)
= f
Small angle approximation sin(
D cos
J
)sin f e »
1,sin e » e
D a = D J sin f cos( d
)
Apply law of cosines cos[90
-
( d +D d
)]
= cos(90
d
)cos(
D q
)
+ sin(90
d
)sin(
D q
)cos f
Small angle approximation (again)
D d = D q cos f
Angular distance in terms of changes in RA and DEC
(
D q
)
2 »
(
D a cos d
)
2 +
(
D d
)
2

Celestial Sphere and Spherical Trigonometry from a rotating platform http://en.wikipedia.org/wiki/Celestial_sphere
"A Compendium of Spherical Astronomy".

Planetarium/Telescope Control Software
Your Phone…