## Starship Distance / Time Calculator

Relativistic Starship Calculator

## Relativistic Time Dilation at Accelerated Velocities (With Side Benefit of Artificial Gravity)

### 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 starship will run more slowly than a clock on Earth according to the equation:

`δTearth = γ·δTship`

### where,

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