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The Time to Fall in a Plunge Orbit
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[QUOTE="Jenab2, post: 6264597, member: 107288"] This equation, t−t₀ = √[d/(2GM)] { √(rd−r²) + d arctan √(d/r−1) } is the classically exact solution to the time-to-fall problem. It does not depend on the acceleration of gravity being constant throughout the fall. Nor does it approximate the resulting time difference by an approximate method of numerical integration. This equation (used twice) can be used in place of the approximation taught in high school physical science class, t₂−t₁ = (t₂−t₀) − (t₁−t₀) where t₀ = the time when the test mass is let go, at distance d from the center of the planet t₁ = the time, during the fall, when the object is at a distance r₁ from the center of the planet (It is permitted that r₁ can be equal to d, but this isn't required.) t₂ = the time, during the fall, when the object is at a distance r₂ from the center of the planet (It is permitted that r₂ can be equal to the radius of the planet, but this isn't required.) [/QUOTE]
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The Time to Fall in a Plunge Orbit
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