Relativistic Star Ship Calculator

for Einstein's universe

by Stephen R. Schmitt

distance:		Light Years	Astronomical Units
acceleration:		Earth G's	Meters/sec/sec
time on earth:		Years	Days
time on board:		Years	Days
maximum speed:		β	fraction of C
maximum kinetic energy:		(γ - 1)·c2	megajoules per kilogram

Contents

1. About
2. The source code
3. Discussion

About

The Relativistic Star Ship Calculator is a Java Script calculator that computes the times to reach distant points with a space vehicle that can accelerate continuously. Such a vehicle can approach but never exceed the speed of light in vacuum, C. The calculator computes travel times for this mission profile:

1. The star ship accelerates continuously from the origin to the midpoint of the mission.
2. At the midpoint, the ship turns its thrusters to face the destination.
3. The ship decelerates continuosly from the midpoint to the destination.

The observed elapsed time of the mission is computed for two cases:

1. for the astronauts in the star ship who are in the moving frame
2. for the clocks at the origin and destination which are in the rest frame

The maximum velocity, V, of the star ship is reached at the midpoint of the mission. The calculator shows this as the ratio of maximum velocity to the speed of light.

Some representative distances:

Planets
Mars                           1.5 AU (Astronomical Units)
Jupiter                        5.2 AU
Saturn                         9.6 AU
Uranus                        19.2 AU
Neptune                       30.0 AU
Pluto                         39.2 AU

nearby stars
Alpha Centauri                 4.3 LY (Light Years)
Barnard's Star                 6.0 LY
Wolf 359                       7.7 LY
Sirius                         8.6 LY
Ross 154                       9.4 LY
Altair                        16.6 LY
Vega                          26.4 LY
Arcturus                      35.8 LY

Milky Way Galaxy
Hyades Star Cluster            150 LY
Betelgeuse                     309 LY
Pleiades Star Cluster          408 LY
Rigel                          913 LY
Crab Nebula                  6,000 LY
Star Cluster M13            21,000 LY   
Center                      30,000 LY

Deep Space
Large Magellanic Cloud     163,000 LY
Small Magellanic Cloud     196,000 LY
Andromeda galaxy         2,000,000 LY
Spiral galaxy M101      25,000,000 LY
Galaxy M87              54,800,000 LY
Perseus cluster        239,000,000 LY
Ursa Major cluster     670,000,000 LY
Quasar 3C 273        1,900,000,000 LY
Quasar 3C 309.1      7,400,000,000 LY
Hubble radius       15,000,000,000 LY

Some constants to consider when using the calculator:

Earth's gravity   = 9.80665 [meters/sec/sec]
astronomical unit = 1.496 x 1011 [meters] {average distance from Sun to Earth}
light year        = 9.460 x 1015 [meters] {distance light travels in one year}

To operate the calculator, first select the desired distance, acceleration, and time units using the radio buttons. Next, enter acceleration and distance quantities that are greater than 0. Last, press the Calculate button. All entries are cleared by pressing the Clear button. On invalid entries, the the output windows will display:

NaN -- Not a Number

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The source code

The Java Script source code for this program can be viewed by using the View|Source command of your web browser.

You may use or modify this source code in any way you find useful, provided that you agree that the author has no warranty, obligations or liability. You must determine the suitability of this source code for your use.

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Discussion

In Einstein's universe, the relativistic effect known as time dilation may allow long journeys in human lifetimes. Time moves more slowly in a moving frame than a stationary frame. A clock in the moving star ship will run more slowly than a clock on Earth according to the equation:

δTearth = γ·δTship

         __________
γ = 1 / √ 1 - v2/c2
v - velocity of the star ship
c - speed of light in vacuum = 299,792,458 [meters/second]

Note that as v gets closer to c, the term γ approaches infinity. The effect of time dilation is negligible at small velocities but increases asymptotically as the velocity of the star ship approaches the speed of light. Note how the kinetic energy becomes extremely large. Besides this, there are many other practical problems in realizing a star ship (such as hitting small dust particles while moving at relativistic velocities). If a practical star ship could be constructed, the term 'astronaut' (which means star-voyager) would be literally correct.

C-ship

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