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for Einstein's universe

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 AU (Astronomical Units) nearby stars Light Years Milky Way Galaxy Light Years Deep Space Light Years
Mars 1.5 Alpha Centauri 4.3 Hyades Star Cluster 150 Large Magellanic Cloud 163,000
Jupiter 5.2 Barnard's Star 6.0 Betelgeuse 309 Small Magellanic Cloud 196,000
Saturn 9.6 Wolf 359 7.7 Pleiades Star Cluster 408 Andromeda galaxy 2,000,000
Uranus 19.2 Sirius 8.6 Rigel 913 Spiral galaxy M101 25,000,000
Neptune 30.0 Ross 154 9.4 Crab Nebula 6,000 Galaxy M87 54,800,000
Pluto 39.2 Altair 16.6 Star Cluster M13 21,000 Perseus cluster 239,000,000
Vega 26.4 Center 30,000 Ursa Major cluster 670,000,000
Arcturus 35.8 Quasar 3C 273 1,900,000,000
Quasar 3C 309.1 7,400,000,000
Hubble radius 15,000,000,000

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

distance Light Yrs 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


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 = γδTship
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.

Copyright 2004, Stephen R. Schmitt