Deadhead

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Deadheading from one solar system to another.

Deadheading is the name given to sublight interstellar travel. The art of flying from one solar system to another at the speed of light under the power of conventional engines.

It is the only way for empires to get to distant stars if the wormhole routes are nonexistent or too dangerous and they haven't acquired warp drive technology yet.

Travel Time

Deadheading to a solar system can take anywhere from half an hour to several hours, depending on the distance to the destination and acceleration of the spacecraft.

Commonly it takes ~10 minutes to reach the speed of light, then 10 minutes per parsec, followed by another ~10 minutes of deceleration.

Acceleration = The acceleration speed of the spacecraft's maneuver drive‎.
Lightspeed = 150'876 m/s
DestinationDistance = Distance to the destination, In meters.

Acceleration to lightspeed in seconds.
AccelerationTime = Lightspeed / Acceleration

Distance traveled during acceleration.
AccelerationDistance = 0.5 * Acceleration * AccelerationTime ^ 2

Total travel time to destination.
DestinationTime = AccelerationTime * 2 + (DestinationDistance - (AccelerationDistance * 2)) / Lightspeed

See dummies.com.