Math 2.0

Astronomy and astrophysics Definition

Spherical astronomy

Builds on Celestial sphereSpherical trigonometryCelestial mechanics

Definition

Spherical astronomy is the branch of astronomy that determines the directions of celestial objects as seen by an observer. Each direction is represented by a point of the celestial sphere. Its subject is the description of these points in coordinate systems and the transformations between such systems. It also studies how the points change with time and with the position of the observer. Its main tool is spherical trigonometry.

Remarks

Example: a typical problem of spherical astronomy is to compute the altitude of a star above the horizon. The data are its right ascension, its declination, the time and the latitude of the observer. It uses the spherical law of cosines in the triangle formed by the celestial pole, the zenith and the star. Non-example: computing the mass of a star from the orbit of a companion is not spherical astronomy, because it needs dynamics and not only directions; it belongs to celestial mechanics. The field is often called positional astronomy, and its high-precision part is called astrometry.

Reading path

To understand this page from the ground up, read these 54 pages in order. The foundations come first.

  1. Celestial sphere concept
  2. Conic section concept
  3. Derivative concept
  4. Differential equation concept
  5. Ellipse concept
  6. Euclidean space object
  7. Euclidean vector concept
  8. First integral concept
  9. Focus of a conic concept
  10. Function concept
  11. Hamiltonian system concept
  12. Interval concept
  13. Ordinary differential equation concept
  14. Spherical trigonometry concept
  15. Velocity concept
  16. Fréchet derivative definition
  17. Kepler problem example
  18. Cross product definition
  19. Ordinary differential equation definition
  20. Function of several variables concept
  21. Vector-valued function concept
  22. Classical mechanics concept
  23. Lipschitz condition definition
  24. n-body problem problem
  25. Momentum concept
  26. Limit of a function of several variables concept
  27. Partial derivative concept
  28. Inertial frame of reference concept
  29. Solution of an ordinary differential equation definition
  30. Continuity in R^n definition
  31. Differentiable function of several variables definition
  32. Newton's laws of motion statement
  33. Partial derivative definition
  34. Initial value problem definition
  35. Differentiable on an open set definition
  36. Gradient definition
  37. Higher partial derivatives definition
  38. Picard–Lindelöf hypotheses definition
  39. Iterated derivative definition
  40. Picard operator definition
  41. C^k function characterised by continuous derivatives statement
  42. Integral equation form of an initial value problem statement
  43. An iterate of the Picard operator is a contraction statement
  44. Vector field definition
  45. Picard–Lindelöf theorem statement
  46. Conservative vector field definition
  47. Classical mechanics definition
  48. Momentum definition
  49. Potential energy definition
  50. Angular momentum definition
  51. Central force definition
  52. Newton's law of universal gravitation statement
  53. Celestial mechanics concept
  54. Spherical astronomy definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Spherical_astronomy
About this page
TagPKPFT9475D
URIm2://PKPFT9475D
Kinddefinition
WritingW0 stub
MSC85A04, 70F15
DefinesSpherical astronomy
UsesCelestial sphere, Spherical trigonometry, Celestial mechanics
Changed3 November 2026

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