PHY216_lect1_2014 - Astrophysics Research Institute

Practical Astrophysics
Lecture 1
Observing the Sky from Earth
Module Leader:
Dr Matt Darnley
Astrophysics Research Institute
Liverpool John Moores University
M.J.Darnley @
Course Lecturer:
Dr Chris Davis
Liverpool Telescope/ARI
Liverpool John Moores University
C.J.Davis @
Liverpool Telescope
The LT is part of the Observatorio del Roque de
Los Muchachos (ORM) which is located on the
summit of La Palma, Altitude 2,363 m
Liverpool Telescope
Notes online
All course materials available on Vital
These Powerpoint slides:
Other good resources online:
Great Circles and Small Circles
Great Circle
• The intersection of a plane
containing the centre of a sphere
and its surface, e.g. ABCD and BEDF.
• P and Q are poles of plane ABCD.
Small Circle
• A circle which does not include
the centre of the sphere, e.g. WXYZ.
On the Earth…
• All lines of Longitude are great circles
• All lines of Latitude are small circles except the equator.
Lines of equal LATITUDE
Lines of equal LONGITUDE
Q. Is the tropic of Cancer a small or a great circle?
Spherical Trigonometry
Spherical triangle
Formed from three arcs of Great Circles. Distances (a; b; c) are measured as angles.
Sum of the 3 angles A + B + C > 180o (this is non-Euclidean geometry appropriate to curved
e.g. if
• arc AB is part of the Earth's equator
• arc CB is the Greenwich Meridian (long=0o)
• arc CA is longitude=90o
then A = B = C = 90o
so A + B + C = 270o in this case.
As the triangle gets small relative to the size of
the sphere then
A + B + C -> 180o
Spherical sine rule:
Spherical cosine rule:
How do these rules relate to Euclidean (plane) geometry?
If the length of the sides are very small (compared to the radius of the sphere),
then sin a ~ a etc. (small angle approximation).
The spherical sine rule then becomes:
The Euclidean cosine rule can also be recovered by the same method.
Celestial Sphere
• Celestial Meridian – a great circle which passes through Zenith and the North & South
celestial poles. It is perpendicular to the horizon.
If you stand facing North, the meridian is a line that passes from north on the horizon, directly
over your head, to south on the horizon behind you
Celestial Sphere
As the earth rotates, stars (like the sun) rise in the east, pass over the meridian (transit), and
set in the west. The hour angle tells you how long it will be before the star transits (or how
much time has passed since it transited!)
• Hour Angle - angle between a star's current position and the meridian (measured
WESTWARD in hours, where 1 hour is equivalent to 15 degrees – because 24 hours = 360
HA ~ 3 hr
An object transits or
culminates when passing
through the meridian. It
has an HA = 0 hr when
culminating. Its HA then
increases as it moves
towards the west. AT HA =
23h it is just one hour
short of culminating
Celestial Sphere
Facing north it’s t’other
way around! The stars rise
on your right and move
towards the left…
HA ~ 21 hr
Celestial Sphere
• Celestial Equator - Projection of
the Earth's equator out onto the
Celestial Sphere.
• Celestial Poles –
we have two of
‘em, a North and
South pole!
• Declination- angular distance of a
star above the Celestial Equator.
Analogous to LATITUDE, hence the
Celestial Equator comprises all
points at zero Declination.
Observing the sky from the surface of the rotating Earth
of stars
Horizon – you can’t
see below this, so
some stars are too far
south to be observed
from e.g. Europe.
Zenith – directly
Altitude – angular
height of star above
the horizon
Zenith distance/angle
– angle between
zenith and direction to
Altitude of the pole above the horizon = latitude of the observer, f (phi)
The Celestial
Star X
Path of Star X on the sky is a
small circle (red) parallel to
the celestial equator (blue).
It rises in the East, transits the
meridian, and sets in the
Star X rises and sets where its
small circle intersects the
observer’s horizon (black).
General rule - for an observer in the NORTH:
• If a northern hemisphere star’s small circle does not intersect the observer’s horizon,
the star never SETS and the star is said to be circum-polar
• If a southern hemisphere star’s small circle does not intersect the observer’s horizon,
the star never RISES
Circumpolar Stars
These objects (at high
declination) never set, and
depend on the observer's
latitude f
For a star that just grazes the
horizon at its lowest elevation,
declination d
is given by:
d = 90o  f
i.e. if
d > 90o - f
then the star is circumpolar
The Latitude of Liverpool is 53o N. Therefore stars with d > 37o never set!
At the north pole, essentially all visible stars are circumpolar; at the equator, none are!
At what declination do stars never rise in Liverpool?
Circumpolar Stars
Upper transit (or culmination)
Lower transit (often below the horizon)
Looking North…
Stars rise in the East and rotate in an anti-clockwise direction.
Skycam-A at the LT
Stars rise and set like
the Sun (well, most of
them do…)
Skycam-A is mounted on
the wall of the telescope
enclosure pointing up at
the roof…
Watch out for Perseid
Meteors towards the
end of the night!
Skycam-T and -Z at the Liverpool Telescope
SkyCam-T : 21o Field of View
SkyCam-Z : 1o Field of View
For more Movies (three every night, in fact) Google Liverpool Telescope
and check out the Night Reports link on the side-bar.
Star Trails
The image on the left shows star trails above the Observatorio del Teide, Tenerife; the image on the right shows
the night sky above UKIRT in Hawaii. Both telescopes are in the northern hemisphere.
But which observatory is furthest north?
Both pictures are facing North – what do the stars do if you look south?
How could you calculate your latitude from these photos?
How can you calculate the duration of the exposure in each photograph?

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