Space Math

Newtonian Constant Acceleration in g's.
Use this to calculate how far a spaceship will go in a certain time at a certain acceleration. A ship going at a rate of 1g for 100 seconds will travel 49000 meters. If you put in distance traveled it will tell you the time needed to travel that distance at the specified g force. G force here is the force of gravity at the earth's surface. This does not take into account relativistic effects, so use this for interplanetary travel
Acceleration Time Distance

Acceleration in g's on a cylinder such as a space station or space colony.
Use this to find out how fast a space station must spin (period of rotation time in seconds) to maintain a certain force of gravity. You can vary the radius to get a new acceleration or vary the period to get a new radius. Changing the g force will recalculate the period. G force here is the force of gravity at the earth's surface.

Period Radius Acceleration

Period and radius of a circular orbit around a planet.
This gives you the distance from the center of planet and the time it takes for one circular orbit. The units are in terms of planet mass. I've given Earth, Jupiter and the sun for examples. (remember the earth is 6,378 km in radius so subtract that out to get distance from the surface.) Click these links to pre load set diameters Earth, Venus, Mars, Jupiter, The Moon

Period Radius Planet Mass

Escape velocity at a planet's surface
This is the speed that will allow an object to leave the gravitational field of a planet. Anything slower will be slowed down enough by gravity to fall backwards to the planet. Radius is is the radius of the planet. Click these links to pre load set diameters Earth, Venus, Mars, Jupiter, The Moon

Velocity Radius Planet Mass

Relativistic effects

Length Contraction.

The length of things shrinks in the direction of the motion. This is measurable at relativistic speeds. Enter the Rest length and a Velocity and get the contracted length. Enter the Contracted length and get the Velocity. How long will a yard stick be at 1/2 the speed of light? The answer is about 2.6 feet. This calculation is based on an Earth Observer.
Velocity Earth length Moving Length

Time Dilation.
At relativistic speeds time slows down. Enter the Rest interval and a Velocity and get the dilated time. For example how long will ten seconds appear to be when traveling at 1/2 C? Answer=11.57 seconds. This is a Little confusing. Time slows down for a fast moving space traveller which means that it looks like more seconds pass on Earth than for the traveller. This calculation is based on an observer from earth.

Velocity Moving Time Earth Time

Long Relativistic Journeys
Going to a star requires that you speed up and then slow down. It is a double calculation. Half of the trip you accelerate, but if you need to slow down for the second half so that you reach the star, not splat against it. A traveler experiences the trip at one time rate and an observer on one of the stars will experience much longer time. At 1 G acceleration, it is possible to travel to a near galaxy within a generation, but when you will come back it will be millions of years later.
Use this calculator to figure the time it takes to get to a star at constant acceleration and then constant deceleration. Counter to what we might expect, a voyager can make it to a star 20 light years away in 6 years. This is not a violation of Relativity, but a side effect.
Note: unlike the other functions I didn't include the calculation where you plug in time and get distance. That acosh got me.
Note 2: If you try for really long distances the trip time shows infinity - this is due to limitations of JavaScript.

Acceleration Distance Trip Time Earth Time

Size of Black Holes

The Swarzchilde radius is calculated as r=2*G*M/c^2. The actual size of black holes is tiny.


Mass Radius

Conversions

Here are some conversions of units which might be used in space travel

Length Conversions

 

Energy Conversions
Chart of Stars closer than 20 light years

The brighter the star, the smaller it's magnitude. The brightest stars have negative magnitudes. Sirius - the dog star - is close by and is very bright. As seen from the earth it has an apparent magnitude of -1.46 making it on of the brightest things in the sky. Most of these stars are not as bright as the sun. They are (on the average) between 4 and 5 light years apart. If you are looking for sun type stars look for Spectral type G with an absolute magnitude of 3 to 5.

Star Name Spectral Type Apparent Magnitude Absolute Magnitude Distance in Light Years
Proxima Centauri M5.5 11.01 15.45 4.22
Alpha Centauri G2 -0.01 4.34 4.40
Alpha Centauri K0 1.35 5.70 4.40
Barnard's Star M5 9.54 13.24 5.94
Wolf 359 M6 13.45 16.56 7.80
Lalande 21185 M2 7.49 10.46 8.31
Sirius A1 -1.44 1.45 8.60
Sirius DA2 8.44 11.33 8.60
L 726-8 M5.5 12.41 15.27 8.73
L 726-8 M5.5 13.25 16.11 8.73
Ross 154 M4.5 10.37 13.00 9.69
Ross 248 M6 12.29 14.79 10.33
Epsilon Eridani K2 3.72 6.18 10.50
Lacaille 9352 M2 7.35 9.76 10.73
Ross 128 M4.5 11.12 13.50 10.89
L 789-6 M5.5 13.3 15.6 11.08
L 789-6 M5 13.3 15.6 11.08
L 789-6 M7 14.0 16.3 11.08
Procyon F5 0.40 2.68 11.41
Procyon DA 10.7 13.0 11.41
61 Cygni K5 5.20 7.49 11.43
61 Cygni K7 6.05 8.33 11.43
Struve 2398 M4 8.94 11.18 11.64
Struve 2398 M5 9.70 11.97 11.64
Groombridge 34 M2 8.09 10.33 11.64
Groombridge 34 M6 11.06 13.30 11.64
G51-15 M6.5 14.81 17.01 11.83
Epsilon Indi K4 4.69 6.89 11.83
Tau Ceti G8 3.49 5.68 11.90
L 372-58 M5.5 13.01 15.17 12.06
L 725-32 M5 12.10 14.25 12.12
Luyten's Star M3.5 9.84 11.94 12.39
Kapteyn's Star M1 8.86 10.89 12.78
Lacaille 8760 M0 6.69 8.71 12.87
Kruger 60 M3 9.85 11.85 13.07
Kruger 60 M6 11.3 13.3 13.07
Ross 614 M4.5 11.12 13.05 13.43
Ross 614 M7 14.6 16.5 13.43
Wolf 1061 M3.5 10.10 11.95 13.91
Wolf 424 M5.5 13.04 14.87 14.05
Wolf 424 M7 13.3 15.1 14.05
CD-37 15492 M4 8.56 10.36 14.22
van Maanen's Star DZ7 12.37 14.15 14.37
L 1159-16 M8 12.28 14.03 14.57
L 143-23 M5.5 13.92 15.66 14.6
DENIS 1048-39 M9 17 19 14.7
LP 731-58 M6.5 15.60 17.32 14.76
BD+68 946 M3.5 9.15 10.87 14.77
CD-46 11540 M3 9.38 11.10 14.80
L 145-141 DQ6 11.50 13.18 15.07
G158-27 M5.5 13.75 15.39 15.33
Ross 780 M5 10.16 11.80 15.34
G208-44 M5.5 13.41 15.04 15.39
G208-44 M6 14.01 15.64 15.39
G208-44 M8 16.66 18.29 15.39
Lalande 21258 M2 8.82 10.40 15.76
Lalande 21258 M6 14.40 15.78 15.76
Groombridge 1618 K7 6.60 8.16 15.89
BD+20 2465 M4.5 9.40 10.95 16.00
L 354-89 M1 8.66 10.19 16.10
LP 944-20 L - - 16.19
DENIS 0255-47 L - - 16.3
CD-44 11909 M3.5 10.94 12.43 16.45
Omicron^2 Eridani K1 4.43 5.92 16.45
Omicron^2 Eridani DA4 9.52 11.01 16.45
Omicron^2 Eridani M4.5 11.17 12.66 16.45
BD+43 4305 M4.5 10.29 11.77 16.47
70 Ophiuchi K0 4.03 5.50 16.59
70 Ophiuchi K5 6.00 7.47 16.59
Altair A7 0.76 2.20 16.77
G9-38 M5.5 14.06 15.47 17.05
G9-38 M5.5 14.92 16.33 17.05
L 722-22 M4 12.03 13.41 17.3
L 722-22 M6 14.3 15.7 17.3
G99-49 M4 11.33 12.68 17.51
G254-29 M4 10.80 12.14 17.59
Lalande 25372 M4 8.46 9.79 17.71
LP 656-38 M3.5 12.15 13.46 17.85
LP 816-60 M5 11.41 12.71 17.91
Stein 2051 M4 11.08 12.37 17.98
Stein 2051 DC5 12.44 13.73 17.98
Wolf 294 M4 9.89 11.18 17.99
Wolf 1453 M1.5 7.97 9.19 18.56
L 347-14 M4.5 12.23 13.45 18.6
Sigma Draconis K0 4.67 5.87 18.81
L 668-21 M1 8.15 9.34 18.83
L 668-21 T - - 18.83
Ross 47 M4 11.56 12.75 18.88
L 205-128 M3.5 10.75 11.93 18.95
Wolf 1055 M3.5 9.12 10.28 19.16
Wolf 1055 M8 17.52 18.68 19.16
L 674-15 M4 12.1 13.3 19.2
Lalande 27173 K5 5.75 6.89 19.26
Lalande 27173 M1 8.07 9.21 19.26
Lalande 27173 M3 10.5 11.6 19.26
Lalande 27173 T - - 19.26
Ross 882 M4.5 11.19 12.32 19.35
CD-40 9712 M3 9.31 10.44 19.35
Eta Cassiopeiae G0 3.46 4.59 19.42
Eta Cassiopeiae K7 7.51 8.64 19.42
Lalande 46650 M2 8.98 10.10 19.47
36 Ophiuchi K1 5.07 6.18 19.52
36 Ophiuchi K1 5.11 6.23 19.52
36 Ophiuchi K5 6.33 7.45 19.47
CD-36 13940 K3 5.32 6.41 19.74
CD-36 13940 M3.5 11.5 12.6 19.74
82 Eridani G5 4.26 5.35 19.77
Delta Pavonis G8 3.55 4.62 19.92
Wolf 1481 M3 11.32 12.39 19.95

 

 

 

 

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