Relativistic Accelerated Linear Motion Type 2 Program by Jay Tanner of Waterloo, NY, USA - 2025

Distance Value and Units Symbol

Acceleration Rate  m/s²

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Double-Click Within Text Area to Select ALL Text ***************************************************************************** RELATIVISTIC LINEAR ACCELERATION STATISTICS FOR IDEALIZED SPACE TRAVEL SIMULATION SCENARIO: Accelerating from rest at rate (a) to distance (D), this program will compute the time required to accelerate to that distance and the speed achieved upon reaching that distance. The program also takes into account the effect of relativistic time dilation so that the rest frame time interval and proper time interval can be compared to see the numerical difference between them. For space travel simulation, the body is usually a virtual spacecraft, but the concept can be applied to ANY moving body and acceleration rate. Even at an everyday low acceleration value, the relativistic time dilation is still taken into account, even though the effect is very, very, very tiny at such ordinary speeds. The program can also be used to compute the falling time for an object in a uniform gravitational field, like close to the Earth's surface, where the distance (D) represents the distance to the ground below and (a) the rate of acceleration toward the ground when released and the speed (v), the speed on impact with the ground. In such cases, any atmospheric friction is ignored. ============================================================================== THE GIVEN DATA: Distance and Acceleration Rate (D, a) D = This is the target distance to be accelerated. It can be given in a variety of units from angstroms to parsecs. = 1.0 LY = 9460730472580800 m = 9.461 quadrillion m = 9.461 trillion km = 5.879 trillion mi ---------------------------------------------------------------------- a = This is the rate of acceleration experienced by the moving body. = 9.80665 m/s² = 32.1740485564304461942257217847769 ft/s² ============================================================================== THE COMPUTATIONS: T = This is the time interval taken to reach distance (D) according to a clock in the relatively static Earth (lab) rest frame. = 625.99951880609715079991701693890987 d 1.71389327530758973524960168908668 y 89wk 2d 23h 59m 18.42484679382911283026352181276799s 2T = 1251.99903761219430159983403387781974 d = 3.42778655061517947049920337817336 y = 178wk 5d 23h 58m 36.84969358765822566052704362553599s ------------------------------------------------------------------------------ t = This is the proper time interval taken to reach distance (D) according to a clock with the moving body. Due to relativistic time dilation, this value will be smaller than the rest frame time interval (T). = 472.49761508565643812869575439125869 d 1.29362796738030510096836619956539 y 67wk 3d 11h 56m 33.94340071625431931317940475081599s 2t = 944.99523017131287625739150878251739 d = 2.58725593476061020193673239913078 y = 134wk 6d 23h 53m 07.88680143250863862635880950249599s ------------------------------------------------------------------------------ Time Diff = This is the time interval difference between the rest frame and the proper time frames while accelerating over the distance (D). = T − t = 153.50190372044071267122126254765118 d = 0.42026530792728463428123548952129 y = 21wk 6d 12h 02m 44.48144607757479351708411706195199s 2(T−t) = 43wk 6d 00h 05m 28.96289215514958703416823412390399s ------------------------------------------------------------------------------ This is the accelerated speed achieved at distance (D). This value cannot exceed the speed of light. v = 260,988,643.347 m/s = 939,559,116.049 km/h = 583,814,968.117 mi/h = 0.87056440674998024089642023962833 c ============================================================================== REFS: c = The speed of light. = 299,792,458 m/s = 1,079,252,848,800 m/h = 299,792.458 km/s = 1,079,252,848.8 km/h = 186,282.397 mi/s = 670,616,629.384 mi/h Light years are based on the standard Julian year of 365.25 days. NOTE: The 32-decimal precision is only for analytical purposes and to see the very small relativistic deviations from the classical Newtonian theory when very small distance values are used.

Double-Click Within Text Area to Select ALL Text ************************************************************************* THERE ARE 18 LENGTH OR DISTANCE UNITS SYMBOLS RECOGNIZED BY THIS PROGRAM: SYMBOL UNITS NAME -------- ------------------------------------------------------------ A Angstroms nm Nanometers um or u Micrometers (or Microns) mm Millimeters cm Centimeters in Inches ft Feet yd Yards m Meters km Kilometers mi Miles (statute) nmi Nautical Miles LS Light Seconds LM Light Minutes LH Light Hours AU Astronomical Units (1 AU = 149,597,870,700 m) LY Light Years (Based on Julian year of 365.25 days) pc Parsecs *************************************************************************

Program by Jay Tanner of Waterloo, NY, USA Revised: Thursday, January 01, 1970 at 12:00:00 AM UTC