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:
The observed elapsed time of the mission is computed for two cases:
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 |
| 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 |
| 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 |
AU -- Astronomical Unit
LY -- Light Year
Some constants to consider when using the calculator:
| Earth's gravity | = 9.80665 [meters/sec/sec] |
| astronomical unit | = 1.496×1011 [meters] {average distance from Sun to Earth} |
| light year | = 9.460×1015 [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 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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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 | |
|
| 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.
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