perihelion

Documentation

Overview

Perihelion: Chapter 38, Planets in Perihelion and Aphelion.

Functions Aphelion and Perihelion implement algorithms from the book to return approximate results.

For accurate results, Meeus describes the general technique of interpolating from a precise ephemeris but does not give a complete algorithm. The algorithm implemented here for Aphelion2 and Perihelion2 is to start with the approximate result and then crawl along the curve at the specified time resolution until the desired extremum is found. This algorithm slows down as higher accuracy is demanded. 1 day accuracy is generally quick for planets other than Neptune.

Meeus doesn't give an algorithm to handle the double extrema of Neptune. The algorithm here is to pick starting points several years either side of the approximate date and follow the slopes inward. The consequence of starting farther from the extremum is that these functions are particularly slow for Neptune. They are offered here though as a simple implementation of Meeus's presentation in the book.

Index

• Constants
• func Aphelion(p int, y float64) (jde float64)
• func Aphelion2(p int, y, d float64, v *pp.V87Planet) (jde, r float64)
• func Perihelion(p int, y float64) (jde float64)
• func Perihelion2(p int, y, d float64, v *pp.V87Planet) (jde, r float64)

Examples

• Aphelion
• Perihelion

Constants

const (
	Mercury = iota
	Venus
	Earth
	Mars
	Jupiter
	Saturn
	Uranus
	Neptune
	EMBary
)

Planet constants for first argument of Perihelion and Aphelion functions.

Functions

func Aphelion

func Aphelion(p int, y float64) (jde float64)

Aphelion returns an approximate jde of the aphelion event nearest the given time.

Argument p must be one of the planet constants above, y is a year number indicating a time near the aphelion event.

Example

package main

import (
	"fmt"
	"math"
	"time"

	"github.com/soniakeys/meeus/v3/julian"
	pa "github.com/soniakeys/meeus/v3/perihelion"
)

func main() {
	// Example 38.b, p. 270
	j := pa.Aphelion(pa.Mars, 2032.5)
	fmt.Printf("%.3f\n", j)
	y, m, df := julian.JDToCalendar(j)
	d, f := math.Modf(df)
	fmt.Printf("%d %s %d at %dʰ\n", y, time.Month(m), int(d), int(f*24+.5))
}

Output:

2463530.456
2032 October 24 at 23ʰ

func Aphelion2

func Aphelion2(p int, y, d float64, v *pp.V87Planet) (jde, r float64)

Aphelion2 returns the aphelion event nearest the given time.

Argument p must be one of the planet constants Mercury through Neptune; EMBary is not allowed. Y is a year number near the perihelion event. D is the desired precision of the time result, in days. V must be a planetposition.V87Planet object consistent with argument p.

Result jde is the time of the event, r is the distance of the planet from the Sun in AU.

func Perihelion

func Perihelion(p int, y float64) (jde float64)

Perihelion returns an approximate jde of the perihelion event nearest the given time.

Argument p must be one of the planet constants above, y is a year number indicating a time near the perihelion event.

Example

package main

import (
	"fmt"
	"math"
	"time"

	"github.com/soniakeys/meeus/v3/julian"
	pa "github.com/soniakeys/meeus/v3/perihelion"
)

func main() {
	// Example 38.a, p. 270
	j := pa.Perihelion(pa.Venus, 1978.79)
	fmt.Printf("%.3f\n", j)
	y, m, df := julian.JDToCalendar(j)
	d, f := math.Modf(df)
	fmt.Printf("%d %s %d at %dʰ\n", y, time.Month(m), int(d), int(f*24+.5))
}

Output:

2443873.704
1978 December 31 at 5ʰ

func Perihelion2

func Perihelion2(p int, y, d float64, v *pp.V87Planet) (jde, r float64)

Perihelion2 returns the perihelion event nearest the given time.

Argument p must be one of the planet constants Mercury through Neptune; EMBary is not allowed. Y is a year number near the perihelion event. D is the desired precision of the time result, in days. V must be a planetposition.V87Planet object consistent with argument p.

Result jde is the time of the event, r is the distance of the planet from the Sun in AU.