Swiss Micros DM42: Time Dilation
Introduction
The program DILATE calculates the time passage from the traveler's perspective:
t' = t * √(1 - (v/c)^2)
where c = Speed of Light = 299,792,458 m/s
We can also state the equation as:
t' = t * cos(arcsin (v/c))
because cos(arcsin(x)) = √(1 - x^2) for |x| ≤ 1
Why cos(arcsin(x)) = √(1 - x^2)?
Let Θ = arcsin x. Then x = sin Θ. Assume that -1 ≤ x ≤ 1.
From the trigonometric identity:
cos^2 Θ + sin^2 Θ = 1
(cos Θ)^2 + (sin Θ)^2 = 1
With sin Θ = x,
(cos Θ)^2 + x^2 = 1
(cos Θ)^2 = 1 - x^2
cos Θ = √(1 - x^2)
cos(arcsin x) = √(1 - x^2)
Swiss Micros DM42 Program: DILATE
Also: Free42, Plus42
00 {52-Byte Prgm}
01 LBL "DILATE"
02 "TIME?"
03 PROMPT
04 "VEL (M/SEC)?"
05 PROMPT
06 299792458
07 ÷
08 ASIN
09 COS
10 ×
11 "T'= "
12 ARCL ST X
13 AVIEW
14 RTN
15 END
Example
A spaceship traveling at a velocity of 186,000,000 m/s (about 416,070,150 mph) for 1 year from our perspective.
XEQ DILATE
TIME? 1
VEL (M/SEC)? 186000000
Result: 0.78426 year would have passed on the spaceship, which is about 9 months and almost 13 days
Until next time,
Eddie
All original content copyright, © 2011-2022. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
