Astronomical Calculations

Returns the instant of first aphelion passage of the specified body following JD as a Julian day number. The current time scale ist taken into account (see TimeScale), meaning the result is either given as ephemeris time or universal time.

The parameter body specifies the planet. Allowed values are: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune.

// add next instant of Mars' aphelion passage to list
Add(Aphelion(Now,Mars));

function AutumnEquinox(Year)

// create a time control list containig the instants of 
// autumnal equnox for the years 1900-2100
var Year: integer;
begin
  for Year:=1900 to 2100 do 
    Add(AutumnEquinox(Year));
end;

function BeginOfBesselianYear(Year)

function Conjunction(JD,Body)

  // assign instant of first conjunction of Jupiter after 1 Jan 2007  
  JD0 := Conjunction(JD('2007-01-01'),Jupiter); 

// create a time control list, containing the instants of Venus'
// greatest eastern eleongations 1900-2100
begin
  TimeScale := UT;
  TimeShift := StdTimeZone;
  JD0 := '1900-01-01';  // starting date
  repeat    
    JD0 := GrEastElongation(JD0,Venus);  // calculate instant
    Add(JD0);                            // add to list
    JD0 := JD0 + VenSynodic - 100.0;     // prepare next calculation
  until YearFromJD(JD0) >= 2100;
  GoTo(Now);
end;

Returns the instant of first lunar apogee passage following JD as a Julian day number. The current time scale ist taken into account (see TimeScale), meaning the result is either given as ephemeris time or universal time.

function LunarNode(JD,Node)

// assign instant of moon's ascending node passage after 1 Jan 1800
// JD0 := LunarNode(JD('1800-01-01'),Ascending);

Returns the instant of first (geocentric) opposition of the specified body following JD as a Julian day number. The current time scale ist taken into account (see TimeScale), meaning the result is either given as ephemeris time or universal time.

The parameter body specifies the planet. Allowed values are: Mars, Jupiter, Saturn, Uranus, Neptune.

Returns the instant of first perihelion passage of the specified body following JD as a Julian day number. The current time scale ist taken into account (see TimeScale), meaning the result is either given as ephemeris time or universal time.

The parameter body specifies the planet. Allowed values are: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune.

function Rise(JD,Body)

Returns the instant of first rise of the specified body within 24 hours following JD. The result is given as a Julian day number in universal time. If the specified body does not rise within 24 hours after JD, the function returns -1. The parameter body may specify the sun, moon, or a planet. Allowed values are: Sun, Moon, Mercury, Venus, Mars, Jupiter, Saturn, Uranus, Neptune.

// create a time control list containig Venus' rise times over a year
var
  year: integer;
  JD  : float;
  JDR : float;  
  i   : integer;
begin
  TimeScale := UT;  // time scale UT
  TimeShift := StdTimeZone;  // use observer's standard time zone information
  year := YearFromJD(Now);   // determine current year
  year := Input(50,150,'Enter year number',year);  // ask for year number (current year is default)
  JD   := JulianDay(year,1,1,0,0,0);               // starting date
  for i:= 1 to 365 do begin                        // 365 days
    JDR := Rise(JD,Sun);        // first rise after JD within 24 hours
    if JDR > 0.0 then begin     // culmination
      Add(JDR);                 // add to list
      JD := JDR + 0.5;          // prepare next calculation
    end else
      JD := JD + 1.0;           // no rise: skip day
  end;
  Goto(Now);
end;

function Set(JD,Body)

Returns the instant of first set of the specified body within 24 hours following JD. The result is given as a Julian day number in universal time. If the specified body does not set within 24 hours after JD, the function returns -1. The parameter body may specify the sun, moon, or a planet. Allowed values are: Sun, Moon, Mercury, Venus, Mars, Jupiter, Saturn, Uranus, Neptune.

function SpringEquinox(Year)

// create a time control list containig the instants of 
// spring equnox for the years 1500-2500
var Year: integer;
begin
  for Year:=1500 to 2500 do 
    Add(SpringEquinox(Year));
end;

function SummerSolstice(Year)

function SupConjunction(JD,Body)