Longitude, Degrees, and Basic Math
Math • 20 minutes
📏 Understanding Longitude (0° to 360°)
Longitude is the position of a planet measured along the ecliptic (the path of the Sun). It's measured in degrees from 0° to 360°.
🌍 Simple Analogy:
Think of longitude like a circular race track. 0° = Start line (Aries), 180° = Halfway point (Libra), 360° = Back to start. Planets move around this track continuously!
📐 Key Points:
- • 0° = Start of Aries
- • 30° = Start of Taurus
- • 60° = Start of Gemini
- • ...
- • 330° = Start of Pisces
- • 360° = Back to 0° (Aries again)
🔢 Converting Longitude to Sign
Since each sign is 30° wide, we can calculate which sign a longitude falls into using simple division.
📐 The Formula:
int() = round down to whole number (floor division)
Sign numbers: 0=Aries, 1=Taurus, 2=Gemini, ..., 11=Pisces
Step-by-Step Examples:
Example 1: Longitude = 304.64°
Step 1: 304.64 ÷ 30 = 10.154...
Step 2: int(10.154) = 10
Step 3: Sign 10 = Aquarius
Example 2: Longitude = 120.79°
Step 1: 120.79 ÷ 30 = 4.026...
Step 2: int(4.026) = 4
Step 3: Sign 4 = Leo
Example 3: Longitude = 359.9°
Step 1: 359.9 ÷ 30 = 11.996...
Step 2: int(11.996) = 11
Step 3: Sign 11 = Pisces (almost back to Aries!)
📐 Calculating Degree in Sign (0° to 30°)
Once we know the sign, we need to know how many degrees into that sign the planet is. This uses the modulo operator (%).
📐 The Formula:
% = modulo (remainder after division by 30)
Result is always between 0° and 30°
Examples:
Example 1: Longitude = 304.64°
Sign: Aquarius (10)
Degree: 304.64 % 30 = 4.64°
Result: Planet is at 4.64° in Aquarius
Example 2: Longitude = 120.79°
Sign: Leo (4)
Degree: 120.79 % 30 = 0.79°
Result: Planet is at 0.79° in Leo (just entered Leo!)
🎯 Complete Example: From Longitude to Full Description
Given: Sun at 304.64°
Step 1: Calculate Sign
Sign = int(304.64 ÷ 30) = int(10.154) = 10
Sign 10 = Aquarius (Kumbha)
Step 2: Calculate Degree in Sign
Degree = 304.64 % 30 = 4.64°
Final Result:
Sun is at 4.64° in Aquarius
Or: "Sun in Aquarius, 4° 38' 24"" (4.64° = 4° + 0.64×60' = 4° 38.4' = 4° 38' 24")
⏱️ Converting Decimal Degrees to Degrees-Minutes-Seconds
Sometimes you'll see positions written as "4° 38' 24"" instead of "4.64°". Here's how to convert:
📐 Conversion Formula:
Given: 4.64°
Degrees = int(4.64) = 4°
Minutes = int((4.64 - 4) × 60) = int(38.4) = 38'
Seconds = ((4.64 - 4) × 60 - 38) × 60 = (38.4 - 38) × 60 = 24"
Result: 4° 38' 24"
🎓 Practice Exercise
Try These Calculations:
- Longitude = 215.4°: Which sign? What degree in sign?
- Longitude = 45.7°: Which sign? What degree in sign?
- Longitude = 0°: Which sign? What degree in sign?
- Longitude = 30°: Which sign? What degree in sign?
Answers:
- Sign 7 (Libra), 5.4°
- Sign 1 (Taurus), 15.7°
- Sign 0 (Aries), 0°
- Sign 1 (Taurus), 0° (start of Taurus)
📝 Key Takeaways
- ✓ Longitude = Position in degrees (0° to 360°)
- ✓ Sign Number = int(Longitude ÷ 30)
- ✓ Degree in Sign = Longitude % 30
- ✓ Each sign = exactly 30° wide
- ✓ These formulas work for any longitude value!