Lecture 2 - Fundamentals of Geodetic Astronomy Flashcards
*Where is geodetic astronomy concerned?
Astronomical latitude (phi), astronomic longitude (lambda), astronomic azimuth (alpha).
Astronomic measurements depend on Earth’s rotation, a precise time system and coordinate and time systems.
What is the apparent motion of a celestial object in astronomy?
The motion caused by the Earth makes the whole sky seem like it is actually rotation.
*What is the celestial sphere?
An imaginary sphere with the Earth at its center. The celestial bodies appear to be located on this sphere, and the sphere appears to rotate around the Earth’s extended axis once every 24 hours carrying the celestial bodies with it overhead and giving them their diurnal motions.
A spherical map of the sky that provides the basis for the coordinate systems used in celestial navigation and in specifying the positions and motions of celestial objects.
A practical tool for astronomy, to plot positions of objects in the sky when their distances are unknown or unimportant.
What are the typical measurements from the observation of a celestial object using a theodolite on the Earth?
Azimuth and Altitude.
How to define the position of a star on the celestial sphere?
To define the position of a star anywhere on the celestial sphere, a direction is needed.
Direction is most simply defined as a unit vector in polar (curvilinear) coordinates : r, theta, lambda. R = 1 (unit vector, as a distance not observed on an infinite celestial sphere). Thus, the vector is defined by only two angles.
All coordinate systems defined here are ‘dynamical’ in nature, though they have recently been replaced by ‘kinematical’ systems designed, in part, to mimic them.
What is the ‘apparent’ coordinate system?
The designation ‘apparent’ will signify that the origin of a celestial coordinate system is at the center of mass of the Earth (geocentric).
What is the ‘heliocentric’ coordinate system?
When ‘apparent’ is not used, the system will be heliocentric – the sun as the center.
The position of a star is different from two observers at different locations on the Earth. Explain.
A celestial coordinate system is defined by the location of its origin and the directions of the axes towards certain characteristic points on the celestial sphere whose positions are defined dynamically using celestial mechanics.
What does the prefix ‘instantaneous’, ‘true’, or ‘mean’ mean when one talks about celestial coordinate systems?
Celestial coordinate systems that are affected by all irregularities and at all frequencies of the rotation axis of the Earth (ie precession and nutation) will be designated as ‘instantaneous’ or ‘true’ and will be shown to be functions of time.
When a celestial system precesses but does not nutate, it will be called ‘mean’.
Is the Earth’s North pole a fixed point? If no, what are the phenomena that cause the irregularities of the rotation axis of the Earth?
No. The irregularities are precession-nutation, diurnal rotation, and polar motion.
What is diurnal rotation?
Around the celestial intermediate pole through the nominal Earth rotation rate and corrections showing variations of the Earth angular velocity.
What is polar motion?
The motion of the celestial intermediate pole with respect to the terrestrial crust.
*What is the Right Ascension System?
The most important celestial system in which star coordinates are published, also serves as the connection between terrestrial, celestial and orbital coordinate systems.
Primary reference plane: the celestial equator.
Secondary plane: the equinoctial colure (the hour circle passing through two polar points NCP and SCP and the vernal and autumnal equinoxes.
Star coordinates: right ascension, alpha, and the declination, delta.
Have a heliocentric origin.
The RA coordinates are time dependent.
*What is the Local Horizon System?
Primary reference plane: the celestial horizon
Secondary plane: the observer’s celestial meridian
Star coordinates: the position of a celestial body (CB) in a system peculiar to a topographically located observer (Altitude & Azimuth).
Altitude h: the angle between the celestial horizon and the point CB measured in the plane of the vertical circle (0-90).
Azimuth a: the angle between the observer’s celestial meridian and the vertical circle through CB (0-360, north to east, clockwise)
Having a terrestrial (topocentric) origin
*What is the hour angle system?
Primary reference plane: the celestial equator
Secondary plane: the hour circle containing the observer’s celestial meridian (the zenith)
Star coordinates: The hour angle t (the angle between the hour circle of CB and the observer’s celestial meridian/hour circle in the plane of the celestial equator: 0-24h, clockwise). The declination delta (the angle between the celestial equator and the point CB in the plane of the hour circle through the point CB:0-90)
Location and time dependent
*What is the ecliptic system?
Primary reference plane: the ecliptic
Secondary plane: the ecliptic meridian plane of the vernal equinox (contains the north and south ecliptic poles, the vernal and autumnal equinoxes)
Star coordinates: The ecliptic latitude beta: the angle between the ecliptic and the normal line to the point CB. The ecliptic longitude lambda: the eastward in the ecliptic plane between the ecliptic meridian of the vernal equinox and the ecliptic meridian of CB
Having a heliocentric origin (can also be defined as geocentric)
How are the right ascension system and ecliptic system related to each other?
LST = RA + LHA
What are the 3 Earth Orientation Parameters (E.O.P.)?
Universal time: stands for the Earth rotation, one revolution in about 24 hours. Due to uneven rotation, UT is not linear w.r.t. atomic time, but proportional to the sidereal time. The excess revolution time is called length of day (LOD).
Coordinates of the Pole: dx and dy coordinates of the celestial ephemeris pole relative to the IERS reference pole IRP.
Celestial Pole Offsets: the observed differences (x, y) w.r.t. conventional CP position.
*What is geodetic astronomy?
One important discipline of geodesy and astronomy; applying astronomy to geodesy.
*Discuss astronomic measurements.
Depend on the Earth’s rotation.
Require a precise time system.
Need coordinate and time systems.
*What is precession?
External torque (due to the Sun, the Moon, and other celestial bodies) exerted on spinning Earth which describes a circular cone with its vertex located at the center of mass of Earth.
*What is nutation?
Produces a secondary perturbation of Earth’s spin axis. due to the inclination of the lunar orbit. Creates period of ~18 years and amplitude 9.81”
