- All Planets Are Earth-Like (at least without Terraforming)
- Faster-Than-Light Travel
- Humanoid Aliens
- Inertial Dampening
- Reactionless Drive
- Single-Biome Planet
- Space Is an Ocean
- Space Pirates
- Stealth in Space (and most of the other subtropes of Space Does Not Work That Way)
- Teleporters and Transporters
- Green-Skinned Space Babe (and Rubber-Forehead Aliens in general)

- v = a * t + v
_{0} - d = 0.5 * a * t
^{2}+ v_{0}* t - 2 * a * d = v
^{2}- v_{0}^{2}

- d = 0.5 * a * t
^{2}+ v_{0}* t1,280,000,000,000 m = 0.5 * 9.8 m/sec^{2}* t^{2}+ 0 * tSimplifying:1,280,000,000,000 m = 4.9 m/sec^{2}* t^{2}

- 1,280,000,000,000 m / 4.9 m/sec
^{2}= t^{2}Simplifying:260,000,000,000 sec^{2}= t^{2}Taking the square root of both sides:510,000 sec = t

- v = a * t + v
_{0}v = 9.8 m/sec^{2}* 510,000 sec + 0v = 5,000,000 m/sec

- d = 0.5 * a * t
^{2}640,000,000,000 m = 0.5 * 9.8 m/sec^{2}* t^{2}Simplifying:640,000,000,000 m = 4.9 m/sec^{2}* t^{2}640,000,000,000 m / 4.9 m/sec^{2}= t^{2}Simplifying:130,000,000,000 sec^{2}= t^{2}Taking the square root of both sides:360,000 sec = t

- v = a * tv = 9.8 m/sec
^{2}* 360,000 secv = 3,500,000 m/sec

- v = a * t + v
_{0}0 = -9.8 m/sec^{2}* t + 3,500,000 m/secSubtracting 3,500,000 m/sec from both sides:-3,500,000 m/sec = -9.8 m/sec^{2}* tDividing both sides by -9.8 m/sec^{2}:-3,500,000 m/sec / -9.8 m/sec^{2}= t360,000 sec = t

- γ = 1 / sqrt (1 - v
^{2}/c^{2})

At rest | γ = 1 |

At 10% of c | γ = 1.005 |

At 50% of c | γ = 1.15 |

At 86.6% of c | γ = 2 |

At 90% of c | γ = 2.29 |

At 99% of c | γ = 7.09 |

At 99.9% of c | γ = 22.37 |

At 100% of c | γ = ∞ |

- T = (c/a) * ArcCosh[a*d/(c
^{2}) + 1] - t = sqrt[(d/c)
^{2}+ (2*d/a)] - v = c * Tanh[a*T/c]
- v = (a*t) / sqrt[1 + (a*t/c)
^{2}] - γ = Cosh[a*T/c]
- γ = a*d/(c
^{2}) + 1

- t = sqrt[(d/c)
^{2}+ (2*d/a)]t = sqrt[(640,000,000,000 m / 300,000,000 m/sec)^{2}+ (2 * 640,000,000,000 m / 9800 m/sec^{2})]t = sqrt[4,550,000 sec^{2}+ 130,600,000 sec^{2}]t = 11,600 sec

- T = (c/a) * ArcCosh[a*d/(c
^{2}) + 1]T = (300,000,000 m/sec / 9800 m/sec^{2}) * ArcCosh[9800 m/sec^{2}* 640,000,000,000 m / ((300,000,000 m/sec)^{2}) + 1]T = (30,600 sec) * ArcCosh[0.06969 + 1]T = 11,360 sec

- v = c * Tanh[a*T/c]v = 300,000,000 m/sec * Tanh[9800 m/sec
^{2}* 11,360 sec / 300,000,000 m/sec]v = 300,000,000 m/sec * 0.3549v = 106,500,000 m/sec

t = c/a * (sqrt [(a*d/c^{2} + γ_{0})^{2}-1] - sqrt[γ_{0}^{2}-1])

- P
^{2}M = A^{3}

- 3.003740720000000000 x 10
^{-6}

- 3.003740720000000001 x 10
^{-6}

- 4.39 x 10
^{-5}A.U.

- P
^{2}* (3 x 10^{-6}) = (4.39 x 10^{-5})^{3}P^{2}* (3 x 10^{-6}) = 8.47 x 10^{-14}P^{2}= (8.47 x 10^{-14}) / (3 x 10^{-6})P^{2}= 2.82 x 10^{-8}P = 1.68 x 10^{-4}years

- Mass of Mars = 6.4 x 10
^{23}kg = 3.2 x 10^{-7}solar massesRadius of orbit = 100 km (orbital altitude) + 3397 km (radius of Mars) = 3497 km = 2.3 x 10^{-5}A.U.P^{2}* (3.2 x 10^{-7}) = (2.3 x 10^{-5}A.U.)^{3}P^{2}= (2.3 x 10^{-5}A.U.)^{3}/ (3.2 x 10^{-7}) = 4 x 10^{-8}P = 2 x 10^{-4}years = 105 minutes.

- Total delta-v = v
_{e}* ln(M/M_{e})

- delta-v = v
_{e}* ln(M/M_{e})7,000,000 m/s = 4500 m/s * ln(M/M_{e})Dividing both sides by the exhaust velocity:(7,000,000 m/s) / (4500 m/s) = ln(M/M_{e})1555 = ln(M/M_{e})To get rid of the natural log, we need to take the natural exponential of both sides:e^{1555}= M/M_{e}

- Nuclear fission (NERVA) engines
- Ion engines, such as those on the
*Dawn*and*Deep Space One*spacecraft - The Orion Drive
- Controlled nuclear fusion engines
- Ground-based laser pushers
- Ramscoops

- delta-v = v
_{e}* ln(M/M_{e})7,000,000 m/s = 6,000,000 m/s * ln(M/M_{e})Dividing both sides by the exhaust velocity:(7,000,000 m/s) / (6,000,000 m/s) = ln(M/M_{e})1.17 = ln(M/M_{e})To get rid of the natural log, we need to take the natural exponential of both sides:e^{1.17}= M/M_{e}

- surface gravitational field strength = G * ρ * 4/3 * π * R

Earth's surface gravity = G * ρ * 4/3 * π * R

... which is, in fact, how fast things accelerate downward near the surface of the Earth when you drop them. Mars, by contrast, only has a radius of 3,380,000 meters and an average density of 3930 kg/m= 6.6738 x 10^{-11} m^{3}/(kg s^{2}) * 5515 kg/m^{3} * 3.14159 * 6,371,000 m

= 9.822 m/s^{2}

- The planet must lie within the Goldilocks Zone for its star.
- The star cannot be too dim, since this will mean its Goldilocks Zone will be too narrow, any planet in the zone will be in synchronous rotation with the star, and the Goldilocks Zone will lie within the Danger Zone for stellar flares.
- If a binary star system, the companion star cannot come closer to the primary than 4 times the Goldilocks Zone distance.
- The star system cannot be metal-poor, or (if its metallicity isn't known) so old that it would have formed when the galactic medium was still metal-poor.
- The planet cannot be too small or light, as this will prevent it from retaining an atmosphere.