The condition/parameter rapidity 1 hyperbolic radian, what the proper velocity dx/dτs unit c?
Condition/Parameter Coordinate velocity v dx/dt in units of c Velocity angle η in i-radians Proper velocity w dx/dτ in units of c Lorentz factor γ dt/dτ = E/mc 2
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1-15314901-1
Momentum = ½mc ⇔ 0.5 map-lightyear/traveler-year 1/√5 ≅ 0.447 ln[(1 + √5)/2] ≅ 0.481 ½ √5/2 ≅ 1.118
Rapidity of 0.5 hyperbolic radian (e − 1)/(e + 1) ≅ 0.462 ½ ½(√e − 1/√e) ≅ 0.521 ½(√e + 1/√e) ≅ 1.128
Momentum = mc ⇔ 1 map-lightyear/traveler-year 1/√2 ≅ 0.707 ln[1 + √2] ≅ 0.881 1 √2 ≅ 1.414
Rapidity of 1 hyperbolic radian (e 2 − 1)/(e 2 + 1) ≅ 0.761 1 ½(e − 1/e) ≅ 1.175 ½(e + 1/e) ≅ 1.543
Kinetic energy = mc 2 ⇔ 2 map-years/traveler-year √3/2 ≅ 0.866 ln[√3 + 2] ≅ 1.317 √3 ≅ 1.732 2
Momentum = 2mc ⇔ 2 map-lightyears/traveler-year 2/√5 ≅ 0.894 ln[2 + √5] ≅ 1.444 2 √5 ≅ 2.236
Rapidity of 2 hyperbolic radians (e 4 −1)/(e 4 +1) ≅ 0.964 2 ½(e 2 − 1/e 2 ) ≅ 3.627 ½(e 2 + 1/e 2 ) ≅ 3.762
table_15314901_1
SELECT Proper velocity w dx/dτ in units of c FROM table WHERE Condition/Parameter = Rapidity of 1 hyperbolic radian
Rapidity of 1 hyperbolic radian