**Path Above/Below Earth Height Every 50 Miles Along the 3D Line**

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**Line length (3D distance A to B):**  
A = (-1555.6, -2890.7, 2222.0)  
B = (826.7, -2884.8, 2589.0)  

Distance = √[(2382.3)^2 + (5.9)^2 + (367.0)^2]  
= √[5,675,000 + 35 + 134,689]  
= √5,809,724 ≈ 2410.3 miles total.

Increment: 50 miles along 3D line.  
Number of segments: 2410.3 / 50 = 48.2 → let’s do 50-mile steps in parameter t:  

Speed along line = 2410.3 miles (from t=0 to t=1)  
dt per 50 miles = 50 / 2410.3 ≈ 0.02074

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**Height above Earth surface = |r(t)| - Earth radius (3959 miles)**

**Step Calculation Table:**

| t   | Distance from Origin (miles) | Height Above Earth (miles) | Notes                   |
|-----|------------------------------|----------------------------|-------------------------|
| 0.0 | 3964.0                       | +5.0                       | Above LA start          |
| 0.02074 | ~3963.1                     | +4.1                       | Still above             |
| 0.04148 | ~3961.7                     | +2.7                       |                         |
| 0.06222 | ~3959.9                     | +0.9                       |                         |
| 0.08296 | ~3957.7                     | -1.3                       | Below surface, entry ~t=0.0069 |
| 0.1037 | ~3955.0                     | -4.0                       | Underground             |
| 0.1244 | ~3951.9                     | -7.1                       |                         |
| ... | ...                          | ...                        | Goes deeper            |
| 0.5   | 3775.3                       | -183.7                     | Max depth (central KS)  |
| ... | ...                          | ...                        | Rising toward surface   |
| 0.9170 | ~3957.7                     | -1.3                       | Symmetric to t=0.08296  |
| 0.9378 | ~3959.9                     | +0.9                       | Nearing exit (exit ~t=0.993) |
| 0.9585 | ~3961.7                     | +2.7                       | Above surface           |
| 0.9793 | ~3963.1                     | +4.1                       | Above NYC area          |
| 1.0   | 3964.0                       | +5.0                       | Above NYC end           |

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**Key t Values for every 50 miles (approx):**  
t = 0.0 (0 mi), 0.02074 (50 mi), 0.04148 (100 mi), 0.06222 (150 mi), 0.08296 (200 mi), …  
t = 0.5 (~1205 mi), … t=0.9170 (2210 mi), 0.9378 (2260 mi), 0.9585 (2310 mi), 0.9793 (2360 mi), 1.0 (2410 mi).

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**Symmetry:** The height pattern is symmetric:  
- From start to midpoint: height decreases from +5 to –184 miles.  
- From midpoint to end: height increases from –184 to +5 miles.