HOLISTIC UNIVERSE MODEL

Calculation Formulas

This page provides Excel formulas for calculating key values at any given year in the Holistic Universe Model. All formulas use a single input: YEAR (e.g., 2000 for J2000).

How to use these formulas: Replace YEAR with your target year (e.g., 2000, -10000, 50000). Negative years represent BCE dates. You can use an Excel translator to translate formulas into your own language.

1. Obliquity (Axial Tilt)

Calculates Earth’s axial tilt in degrees at any given year.

EXCEL FORMULA OBLIQUITY IN DEGREES (Change the YEAR value)


=23.41398+(-0.633849*(COS(RADIANS(((YEAR--301340)/(333888/3))* 360))))+(0.633849*(COS(RADIANS(((YEAR--301340)/(333888/8))*360))))

Components:

23.41398 — Mean obliquity (degrees)
0.633849 — Amplitude of variation (degrees)
333888/3 — Inclination precession cycle (111,296 years)
333888/8 — Obliquity cycle (41,736 years)
-301340 — Anchor year (start of current Holistic-Year cycle)

Example Values:

Year	Obliquity
2000 AD	23.439°
-10000 (10,000 BCE)	24.23°
+10000 (10,000 AD)	22.41°

2. Eccentricity

Calculates Earth’s orbital eccentricity in AU at any given year.

EXCEL FORMULA ORBITAL ECCENTRICITY IN AU (Change the YEAR value)


=IF((0.0153869+((-0.0014226+((-0.0000659)*(SIGN(COS(RADIANS(((YEAR--301340)/(333888/16))*360)))*ABS(COS(RADIANS(((YEAR--301340)/(333888/16))*360)))^(0.8))))*(COS(RADIANS(((YEAR--301340)/(333888/16))*360)))))>0.0153869,(0.0153869+((-0.0014226+((-0.0000659)*(SIGN(COS(RADIANS(((YEAR--301340)/(333888/16))*360)))*ABS(COS(RADIANS(((YEAR--301340)/(333888/16))*360)))^(0.8))))*(COS(RADIANS(((YEAR--301340)/(333888/16))*360))))),(0.0153869+((-0.0014226+((-0.0000659)*((COS(RADIANS(((YEAR--301340)/(333888/16))*360)))*ABS(COS(RADIANS(((YEAR--301340)/(333888/16))*360)))^(0.8))))*(COS(RADIANS(((YEAR--301340)/(333888/16))*360))))))

Components:

0.0153869 — Mean eccentricity
333888/16 — Perihelion precession cycle (20,868 years)

Example Values:

Year	Eccentricity
2000 AD	~0.01671
Minimum	~0.0139
Maximum	~0.0167

3. Inclination to Invariable Plane

Calculates Earth’s orbital inclination relative to the solar system’s invariable plane in degrees.

EXCEL FORMULA INCLINATION TO THE INVARIABLE PLANE IN DEGREES (Change the YEAR value)


=1.481592+(-0.633849*(COS(RADIANS(((YEAR--301340)/(333888/3))*360))))

Components:

1.481592 — Mean inclination (degrees)
0.633849 — Amplitude of variation (degrees)
333888/3 — Inclination precession cycle (111,296 years)

Example Values:

Year	Inclination
2000 AD	~1.58°
Maximum	~2.115°
Minimum	~0.848°

4. Longitude of Perihelion

Calculates the longitude of perihelion (direction of Earth’s closest approach to the Sun) in degrees.

EXCEL FORMULA LONGITUDE OF PERIHELION IN DEGREES (Change the YEAR value)


=((5.05*(SIN(RADIANS(((IF(((YEAR--301340)/(333888/16))>1,(YEAR--301340),((YEAR--301340)-(ROUNDDOWN((YEAR--301340)/(333888/16),0)* (333888/16)))))/(333888/16))*360))))+(270+((YEAR--301340)* (360/(333888/16))))-(ROUNDDOWN((270+((YEAR--301340)* (360/(333888/16))))/360,0)*360)+(2.4587* (SIN(RADIANS(((IF(((YEAR--301340)/(333888/16))>1,(YEAR--301340),((YEAR--301340)-(ROUNDDOWN((YEAR--301340)/(333888/16),0)* (333888/16)))))/((333888/16)/2))*360)))))

Key Values:

Year	Longitude
1246 AD	90° (aligned with December solstice)
2000 AD	~102.95°
22,114 AD	90° (next December solstice alignment)

5. Length of Days & Years

These formulas explain the connection between all day and year lengths.

Solar Year (in days)

EXCEL FORMULA LENGTH OF SOLAR YEAR IN DAYS


=365.242188997508-(2.29/86399.9886961896)*(<Current obliquity>-23.41398)

Where <Current obliquity> is calculated using the obliquity formula above.

Sidereal Year (in days)

EXCEL FORMULA LENGTH OF SIDEREAL YEAR IN DAYS


=(365.242188997508*(333888/13)/((333888/13)-1)) + ((-3058 / 86399.9886961896) * (<Current eccentricity>-0.015321))

Where <Current eccentricity> is calculated using the eccentricity formula above.

Sidereal Year (in seconds)

The sidereal year in SI seconds is fixed:


31,558,149.724 SI seconds

Day Length (in SI seconds)

EXCEL FORMULA LENGTH OF DAY IN SI SECONDS


=31558149.724/<Current sidereal year in days>

6. Precession Durations

With the help of the above formulas and the coin rotation paradox, we can calculate all precession durations.

Axial Precession

EXCEL FORMULA LENGTH OF AXIAL PRECESSION IN YEARS


=<Sidereal year (days)>/(<Sidereal year (days)>-<Solar year (days)>)

Perihelion Precession

EXCEL FORMULA LENGTH OF PERIHELION PRECESSION IN YEARS


=<Axial precession>*13/16

Inclination Precession

EXCEL FORMULA LENGTH OF INCLINATION PRECESSION IN YEARS


=<Axial precession>*13/3

Anomalistic Year (in days)

EXCEL FORMULA LENGTH OF ANOMALISTIC YEAR IN DAYS


=((<Perihelion precession in years>*<Solar year (days)>)/(<Perihelion precession in years>-1))

Where:

<Sidereal year (days)> = length of sidereal year in days
<Solar year (days)> = length of solar year in days
<Axial precession> = Axial precession duration in years
<Perihelion precession in years> = Perihelion precession duration in years

How the Formulas Connect

All formulas are interconnected through the Holistic-Year (333,888 years) and its Fibonacci divisions:

Cycle	Divisor	Duration (years)	Used In
Holistic-Year	1	333,888	All calculations
Inclination Precession	3	111,296	Obliquity, Inclination
Obliquity Cycle	8	41,736	Obliquity
Axial Precession	13	25,683.69	Longitude of perihelion
Perihelion Precession	16	20,868	Eccentricity, Day/Year lengths


┌─────────────────────────────────────────────────────────────────┐
│                HOLISTIC-YEAR (333,888 years)                    │
├─────────────────────────────────────────────────────────────────┤
│                              │                                  │
│         ÷3 = 111,296        │         ÷13 = 25,684             │
│    (Inclination Precession)  │     (Axial Precession)           │
│              │               │              │                   │
│              ▼               │              ▼                   │
│         Inclination          │      Longitude of                │
│           Formula            │       Perihelion                 │
│              │               │              │                   │
│              ▼               │              │                   │
│         ÷8 = 41,736    ◄─────┼──────────────┤                   │
│       (Obliquity Cycle)      │              │                   │
│              │               │              ▼                   │
│              ▼               │       ÷16 = 20,868               │
│          Obliquity           │    (Perihelion Precession)       │
│           Formula            │              │                   │
│                              │              ▼                   │
│                              │    Eccentricity, Day Length      │
│                              │      Year Lengths                │
└─────────────────────────────────────────────────────────────────┘

Verification

To verify these formulas, compare results against:

J2000 Values (Year = 2000):
- Obliquity: 23.439° (IAU: 23.439291°) ✓
- Eccentricity: 0.01671 (NASA: 0.01671022) ✓
- Longitude of perihelion: 102.95° (NASA: 102.94719°) ✓
Historical Values:
- Obliquity at -10,000: 24.23° (Laskar: 24.23°) ✓
- Perihelion aligned with December solstice at 1246 AD ✓
3D Simulation:
- Use the Interactive 3D Simulation to verify values visually
- Console tests (F12) compare model values against IAU references

Excel Spreadsheet

The spreadsheet with all formulas and interactive calculations is available. Click the PURPLE Data Button at the top of any page to access a simplified view.

Return to Mathematical Foundations or explore the Appendix for reference data.