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Escape Velocity
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_keyMaster ≡ _gateKeeper
_gateKeeper =
The end point of a 69.2 mile long line tangent above the Earth's surface. The Earth's radius 𝑅, The tangent line 𝑑 = 69.2 miles. The line from Earth's center to the end of the tangent 𝑅 = 3 , 958.8 miles (Earth's radius) 𝑑 = 69.2 miles (length of tangent line) ℎ = height above Earth's surface at the end of the line. ( 𝑅 + ℎ ) 2 = 𝑅 2 + 𝑑 2. ℎ : 𝑅 + ℎ = 𝑅 2 + 𝑑 2 ℎ = 𝑅 2 + 𝑑 2 − 𝑅. ℎ = ( 3 , 958.8 ) 2 + ( 69.2 ) 2 − 3 , 958.8 ℎ = 15 , 674 , 000 + 4 , 790 − 3 , 958.8 ≈ 15 , 678 , 790 − 3 , 958.8 ℎ ≈ 3 , 959.67 − 3 , 958.8 = altitude 0.87 miles = 4,593.6 feet. The straight-line distance between the endpoints of an 83.5-mile-long 1-degree arc on Earth is approximately 69.1 miles.
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