Index

argument of perihelion

11: Photographic Astrometry

Astrometry

B

Besselian coefficients

1.10: 1.10- Besselian Interpolation

C

Calculating Surface Integrals

5.6: Calculating Surface Integrals

celestial equator

celestial sphere

6: The Celestial Sphere

circular hyperboloid

16.1: Introduction
16.6: The Collinear Lagrangian Points

Collinear Lagrangian Points

cones

2.6: The General Conic Section

conic sections

2: Conic Sections
2.5: Conic Sections
2.6: The General Conic Section

Conjugate Diameters

9.2: Kepler's Second Law from Conservation of Angular Momentum

Conservation of angular momentum

Contact Transformations

14.2: Contact Transformations and General Perturbation Theory

Cramer's rule

1.7: Simultaneous Linear Equations, N = n

cylinder

4.6: The Cylinder

cylindrical coordinates

D

direction ratios

Directional cosines

5.10: Nabla, Gradient and Divergence

directrix

2.3: The Parabola

Div

dynamical ellipticity

6.7: Precession

E

eccentric anomaly

eccentricity

Ecliptic Coordinates

6.5: Ecliptic Coordinates

ellipse

2.2: The Ellipse
2.6: The General Conic Section

Ellipsoid

4.3: The Ellipsoid

Elliptic Orbit

ellipticity

epoch of osculation

9.9: Osculating Elements

Equatorial Coordinates

3.7: Rotation of Axes, Three Dimensions. Eulerian Angles

equivalent potential

16.1: Introduction

Eulerian angles

F

First Point of Aries

6.7: Precession

G

Gauss's Law (Gravity)

5.5: Gauss's Theorem

Gaussian constant

13.4: Kepler's Second Law

Gaussian quadrature

1.15: Gaussian Quadrature - the Algorithm

geocentric equatorial coordinates

13.5: Coordinates

geoid

4.3: The Ellipsoid

Grad

5.10: Nabla, Gradient and Divergence

gravitational constant, G

5.3: Newton's Law of Gravitation

gravitational field

5.2: Gravitational Field

greatest western elongation

8.2: Opposition, Conjunction and Quadrature

Gregorian Calendar

6.9: The Length of the Year

H

heliocentric ecliptic

13.5: Coordinates

heliocentric equatorial coordinates

13.5: Coordinates

Hooke’s law

16.4: Hooke's Law

hyperbola

2.4: The Hyperbola
2.6: The General Conic Section

hyperbola of revolution

9.7: Position in a Hyperbolic Orbit
10.6: Elements of a Hyperbolic Orbit

Hyperbolic Orbit

Hyperboloid

8.2: Opposition, Conjunction and Quadrature

I

inferior planets

K

Kepler’s first law

9.1: Kepler's Laws
9.4: Kepler's First and Third Laws from Newton's Law of Gravitation

Kepler’s second law

9.1: Kepler's Laws

Kepler’s third law

9.1: Kepler's Laws
9.4: Kepler's First and Third Laws from Newton's Law of Gravitation

Kepler's Second Law

9.2: Kepler's Second Law from Conservation of Angular Momentum
13.4: Kepler's Second Law

L

Lagrange Interpolation

1.11: Fitting a Polynomial to a Set of Points - Lagrange Polynomials and Lagrange Interpolation

Lagrange Polynomials

1.11: Fitting a Polynomial to a Set of Points - Lagrange Polynomials and Lagrange Interpolation

Lagrange’s Planetary Equations

14.4: Lagrange's Planetary Equations

Lagrangian Points

16.1: Introduction
16.6: The Collinear Lagrangian Points

latera recta

2.4: The Hyperbola

lattitude

latus rectum

6.9: The Length of the Year

leap year

Legendre Polynomials

1.14: Legendre Polynomials
5.11: Legendre Polynomials

longitude

5.12: Gravitational Potential of any Massive Body

M

Moments of Inertia

N

Nabla

5.10: Nabla, Gradient and Divergence

Newton's Law of Gravitation

5.3: Newton's Law of Gravitation

Nonlinear Simultaneous Equations

1.9: Nonlinear Simultaneous Equations

Nutation

6.8: Nutation

nutation in longitude

6.8: Nutation

nutation in the obliquity

6.8: Nutation

O

oblate symmetric top

14.5: Motion Around an Oblate Symmetric Top

Obliquity of the Ecliptic

6.5: Ecliptic Coordinates

optical double (binary stars)

17.1: Introduction to Visual Binary Stars

optical pair (binary stars)

17.1: Introduction to Visual Binary Stars

Orbital elements

9.8: Orbital Elements and Velocity Vector
14.3: The Poisson Brackets for the Orbital Elements

osculating orbits

9.9: Osculating Elements

Oumuamua

9.7: Position in a Hyperbolic Orbit

P

parabola

2.6: The General Conic Section

Parabolic Orbit

9.6: Position in a Parabolic Orbit

Paraboloid

4.4: The Paraboloid

Plane Triangles

3.2: Plane Triangles

Poisson Brackets

14.3: The Poisson Brackets for the Orbital Elements

Precession

6.7: Precession

prograde motion

17.3: The Elements of the True Orbit

R

radial velocity

18.7: Measuring the Radial Velocity

radius vector

8.4: Direct and Retrograde Motion, and Stationary Points
17.3: The Elements of the True Orbit

refraction

11.3.3: Refraction

retrograde motion

Rotation of Axes

3.6: Rotation of Axes, Two Dimensions

S

sector ratios

13.3: Sectors

Sectors

13.3: Sectors

semi transverse axis

sidereal hours

8.3: Sidereal and Synodic Periods

Sidereal periods

sidereal year

6.9: The Length of the Year
8.3: Sidereal and Synodic Periods

Simpson's rule

1.2: Numerical Integration

South Celestial Pole

18.1: Introduction to Spectroscopic Binary Stars

Spectroscopic Binary Stars

Spherical coordinates

8.4: Direct and Retrograde Motion, and Stationary Points

Spherical Triangles

3.5: Spherical Triangles

Stationary Points

summer solstice

6.5: Ecliptic Coordinates

superior planets

8.2: Opposition, Conjunction and Quadrature

synodic periods

8.3: Sidereal and Synodic Periods

T

triangle ratios

13.3: Sectors
13.12: Sector-Triangle Ratio

triangles

13.2: Triangles

True anomaly