Satellite Geodesy part 1

1. What is the complete conceptual definition of how a coordinate system is formed?

Reference system.

2. What defines the origin and orientation of a coordinate system’s fundamental planes or axes?

Reference system.

3. What includes the fundamental mathematical and physical models underlying a coordinate system?

Reference system.

4. What is the practical realization of a reference system through observations?

Reference frame.

5. What consists of identifiable fiducial points in the sky or on Earth’s surface?

Reference frame.

6. What is described by a catalogue of precise positions and motions at a specific epoch?

Reference frame.

7. What reference system explicitly specifies all models, numerical constants, and algorithms?

Conventional reference system.

8. What two fundamental reference systems are required in satellite geodesy?

Conventional inertial reference system (CIS) and conventional terrestrial reference system (CTS).

9. Is the conventional inertial reference system (CIS) space-fixed or Earth-fixed, and what does it describe?

Space-fixed; it describes satellite motion.

10. Is the conventional terrestrial reference system (CTS) space-fixed or Earth-fixed, and what does it describe?

Earth-fixed; it describes observation-station positions and satellite-geodesy results.

11. What two considerations can define a celestial reference system (CRS)?

Kinematic or dynamic considerations.

12. What CRS is defined by stars or quasars with well-known positions and measurable proper motions?

Kinematic CRS.

13. What CRS is based on the motion of planets, the Moon, or artificial satellites?

Dynamical CRS.

14. What are the origin and axis orientations of the celestial reference system described in the reviewer?

Origin: Earth’s centre of mass; X-axis: mean equinox at J2000.0; Z-axis: orthogonal to the mean equator at J2000.0; Y-axis: completes a right-handed system.

15. What spherical coordinates usually describe star positions, and what radius is assumed?

Right ascension (α) and declination (δ); a unit radius.

16. What corrections account for stellar motion, changes in Earth’s rotation axis, observer displacement, Earth’s orbital motion, and atmospheric bending?

Proper motion; precession and nutation; parallax; aberration; refraction, respectively.

17. What is the practical realization of a CRS, and what technique observes its extragalactic radio sources?

Celestial Reference Frame (CRF); Very Long Baseline Interferometry (VLBI).

18. What are the alternative name, origin, pole, principal-axis direction, and rotation of the terrestrial reference system?

Earth-Centred, Earth-Fixed (ECEF); Earth’s centre of mass; Conventional Terrestrial Pole (CTP); X-axis toward the intersection of the mean Greenwich meridian and equator; follows Earth’s diurnal rotation.

19. What organization maintains the conventional terrestrial reference system, and what are the system and its realization called?

International Earth Rotation and Reference Systems Service (IERS); International Terrestrial Reference System (ITRS); International Terrestrial Reference Frame (ITRF).

20. What are the defining characteristics of ITRS?

Geocentric, including oceans and atmosphere; SI metre with scale consistent with relativistic gravitation; initial BIH orientation at epoch 1984.0; no-net-rotation condition relative to Earth’s crust.

21. How is ITRF realized, what ellipsoid is recommended, and what define its Z-axis and X-axis?

Cartesian coordinates and linear velocities of global observing sites; GRS80 ellipsoid; Conventional Terrestrial Pole (CTP) and Greenwich Meridian Origin (GMO), respectively.

22. What provides a unified global basis for geodetic observations and estimated parameters?

International Terrestrial Reference Frame (ITRF).

23. What comprises markers attached to Earth’s solid crust with precisely determined three-dimensional positions and motions?

International Terrestrial Reference Frame (ITRF).

24. According to the reviewer’s answer key, how often is a new ITRF realized?

Nearly every year.

25. What technique combines radio antennas to function as a telescope with a very large effective diameter?

Very Long Baseline Interferometry (VLBI).

26. What technique uses ultrashort laser pulses to measure round-trip travel time to orbiting retroreflectors?

Satellite Laser Ranging (SLR).

27. What are laser-ranging measurements to Earth-orbiting targets and lunar targets called?

Satellite Laser Ranging (SLR) and Lunar Laser Ranging (LLR), respectively.

28. What technique provides unambiguous millimetre-precision ranges for determining satellite orbits and station positions and motions?

Satellite Laser Ranging (SLR).

29. What approximate satellite-altitude range can SLR support, according to the reviewer?

Approximately 300 km to geosynchronous altitude of 36,000 km.

30. What navigation systems correspond to GPS, GLONASS, China’s system, and Japan’s system?

Global Positioning System (GPS); GLObal NAvigation Satellite System (GLONASS); BeiDou/Compass; Quasi-Zenith Satellite System (QZSS).

31. What system was developed for precise orbit determination and accurate positioning of ground beacons?

DORIS: Doppler Orbitography by Radiopositioning Integrated on Satellite.

32. What does DORIS measure, what link direction does it use, and where are its receivers and transmitters?

Doppler shift; uplink; receivers aboard satellites and transmitters on the ground.

33. What complicates terrestrial reference-frame establishment, and what coordinate and modelling precision levels are stated?

Crustal deformations; station-coordinate precision of 1 cm or better; deformation modelling at the millimetre level.

34. According to the answer key, what operations transform coordinates between celestial and terrestrial frames?

Rotations corresponding to precession, nutation, and pole movement.

35. What is the slow wandering of Earth’s rotation axis relative to the solid Earth called?

Polar motion.

36. What are the approximate cycle, name, and displacement of the largest polar-motion component, and which axis uses a stable average pole?

430-day cycle; Chandler Period; displacement generally no more than 12 m; Z-axis.

37. What describe the periodic and long-term motions of Earth’s spin axis in space?

Nutation and precession.

38. Relative to what distant objects does Earth’s axis change direction, how long is its precession cycle, and what produces its smaller “bumpy” motions?

Quasars; approximately 26,000 years; precession produces the long-term motion, while nutation produces smaller motions.

39. What is the reviewer’s transformation equation from CRF coordinates to TRF coordinates?

[TRF] = R_M(t) R_S(t) N(t) P(t) [CRF].

40. What is the inverse transformation from TRF coordinates to CRF coordinates?

[CRF] = Pᵀ(t) Nᵀ(t) R_Sᵀ(t) R_Mᵀ(t) [TRF].

41. In the CRF-to-TRF transformation, what do P, N, R_S, and R_M represent, and which pairs transform through CEP?

P: precession; N: nutation; R_S: Earth rotation about the CEP axis; R_M: polar motion. P and N transform CRF to CEP; R_S and R_M transform CEP to TRF.

42. What does CEP stand for?

Conventional Ephemeris Pole.

43. What do precession and nutation transform the J2000.0 mean equator and equinox into, and how are the resulting axes oriented?

True equator and equinox at the observation epoch; Z-axis toward the CEP; X-axis toward the true Aries point.

44. What are the shape, Earth’s location, nearest and farthest points, apsidal line, and size-and-shape parameters of a satellite orbit?

Orbital ellipse; Earth’s centre of gravity at one focus; perigee and apogee; line of apsides along the major axis; semi-major axis and eccentricity.

45. What are the orbital terms for south-to-north equator crossing, the opposite crossing, orbital tilt, ascending-node-to-perigee angle, equinox-to-ascending-node angle, and Greenwich-meridian-to-equinox angle?

Ascending node; descending node; inclination; argument of perigee; right ascension of the ascending node; Greenwich hour angle of the vernal equinox.

46. Why are geocentric coordinates inconvenient for surveyors?

Their values are large; their axes do not directly represent local north–south and east–west directions; they do not directly indicate relative elevations.

47. Into what coordinates are geocentric coordinates commonly converted for practical use?

Geodetic coordinates: latitude (φ), longitude (λ), and height (h).

48. How are geodetic heights converted to orthometric heights?

Subtract geoid height from geodetic height: H = h − N.

49. What describes the relationship between a particular local ellipsoid and a global geodetic reference system?

Geodetic datum.

50. According to the reviewer, what five parameters define a geodetic datum, and when is it called an absolute datum?

Semi-major axis (a), flattening (f), and origin offsets ΔX, ΔY, ΔZ; an absolute datum has ΔX = ΔY = ΔZ = 0.

51. What three groups of time scales are important in satellite geodesy, and what are their purposes?

Sidereal or Universal Time: Earth’s orientation relative to a space-fixed frame; Ephemeris, Dynamical, or Terrestrial Time: satellite equations of motion; Atomic Time: precise signal-travel-time measurement.

52. What underlies time scales, what is a time unit, and what is the usual basic unit?

Uniform, repetitive astronomical or physical phenomena; a multiple or fraction of the scale measure; the second, from which larger units are derived.

53. Within what must a starting point or origin be fixed, often using an astronomical event?

A time scale.

54. What are datation, epoch, absolute time measurement, relative time measurement, and time-tagging?

Datation assigns a time-scale reading to an event; epoch is the observation instant; absolute measurement determines an epoch; relative measurement determines an interval and is often more accurate; time-tagging records an event’s transmission or reception instant.

55. What angle measures Earth’s rotation using the meridian of a celestial body and a reference meridian?

Hour angle.

56. What time is defined by the Greenwich hour angle of a fictitious mean Sun, augmented by 12 hours?

Universal Time.

57. What time is defined by the vernal equinox’s hour angle, and what are its mean and true forms?

Sidereal time; mean sidereal time uses the mean equinox; true or apparent sidereal time uses the true equinox.

58. Why are solar and sidereal time nonuniform, and what denotes Universal Time corrected for polar motion?

Earth’s rotation rate is not constant because of tidal deformation, other mass transports, and rotation-axis variations; UT1.

59. What are time systems derived from planetary motions in the solar system called?

Dynamic times.

60. According to the reviewer’s terminology, what inertial time system supplies the time variable in the equations of motion?

Barycentric Dynamic Time (BDT).

61. According to the reviewer, what quasi-inertial time system is used to integrate satellite orbital equations around Earth, and what was it formerly called?

Terrestrial Dynamic Time (TDT); formerly Ephemeris Time.

62. In what year did the IAU introduce Terrestrial Time to replace TDT, and what is its abbreviation?

1991; TT.

63. How is dynamical time realized in practice, what unit does UTC use, and how is UTC kept close to UT1?

Using an atomic time scale; the atomic second; insertion of integer leap seconds at specified epochs.

64. From what epoch does Julian Date count elapsed mean solar days?

January 1.5, 4713 BC, meaning noon on January 1.

65. How is Modified Julian Date calculated, and when does its day begin?

MJD = JD − 2,400,000.5; its day begins at civil midnight.

66. What are the civil date and Julian Date of the J2000.0 standard epoch?

January 1, 2000, at 12:00 TT; JD 2,451,545.0.

67. What are the civil date and Julian Date of the GPS standard epoch?

January 6, 1980, at 00:00; JD 2,444,244.5.

68. What is the distance from the reference ellipsoid to a surface point measured along the ellipsoidal normal called?

Ellipsoidal height or geodetic height, symbolized h.

69. When is ellipsoidal height positive or negative, and along what direction is it measured?

Positive when the point is above the ellipsoid; negative when below it; measured along the ellipsoidal normal, which generally differs from the plumb line.

70. What gravitational quantity is related to an object’s height, and what surfaces have equal gravitational potential?

Potential energy; equipotential surfaces.

71. What defines the geoid, why is it irregular, and what two properties describe gravity at a point?

Gravity defines the geoid; uneven mass distribution and Earth’s nonspherical shape produce variations; gravity has direction and magnitude.

72. What is geoid height, what is its symbol, and how is its sign determined?

The separation from the reference ellipsoid to the geoid along the ellipsoidal normal; N; positive where the geoid is above the ellipsoid and negative where it is below.

73. How do ellipsoidal height, orthometric height, and geoid height differ, and what equation relates them?

Ellipsoidal height (h) is measured from the ellipsoid along its normal; orthometric height (H) is measured from the geoid along a plumb line; geoid height (N) is the geoid–ellipsoid separation; H = h − N.