To travel between the stars it is necessary to be able to accelerate an interstellar probe to some very fast speed, let it travel through space (without friction, it will keep going due to energy), and then decelerate it once it arrives at the target destination. Space is insanely large and to get most places you really want to be traveling at a significant fraction of the speed of light; however, this requires enormous amounts of energy since by special relativity, the faster you are travelling, the more energy is required to accelerate further. This enforces the limit that you cannot go faster than the speed of light since this would require infinite energy.)
This formula is linear in mass (m) and considerably superlinear in velocity (v) approaching infinity as velocity approaches the speed of light (c).
The y-axis is incremented in units of 100 million gigajoules (=10^17 joules). Even accelerating a 1kg mass to 10% the speed of light requires 4.5*10^14 joules. 50% of c requires 1.4*10^16 joules.
For comparison, world energy consumption in 2013 was estimated by the International Energy Association to be 5.67x10^20 joules. In other words, accelerating a single 5 tonne probe to 10% c would require ~1% of Earth’s entire energy consumption. Accelerating to 80% could required 100% of 2013’s energy consumption. Now consider that to colonize the universe, we need to send upwards of 100 million (10^8) probes.
Since we need to both accelerate and decelerate a probe, this energy is required twice over. Doubling the mass of the probe doubles the energy required, but doubling the target speed multiplies the energy required many times over even at very small fractions of the speed of light.
Energy Required to Accelerate Mass
To travel between the stars it is necessary to be able to accelerate an interstellar probe to some very fast speed, let it travel through space (without friction, it will keep going due to energy), and then decelerate it once it arrives at the target destination. Space is insanely large and to get most places you really want to be traveling at a significant fraction of the speed of light; however, this requires enormous amounts of energy since by special relativity, the faster you are travelling, the more energy is required to accelerate further. This enforces the limit that you cannot go faster than the speed of light since this would require infinite energy.)
The relativistic kinetic energy of a rigid body is given by:
This formula is linear in mass (m) and considerably superlinear in velocity (v) approaching infinity as velocity approaches the speed of light (c).
The y-axis is incremented in units of 100 million gigajoules (=10^17 joules). Even accelerating a 1kg mass to 10% the speed of light requires 4.5*10^14 joules. 50% of c requires 1.4*10^16 joules.
For comparison, world energy consumption in 2013 was estimated by the International Energy Association to be 5.67x10^20 joules. In other words, accelerating a single 5 tonne probe to 10% c would require ~1% of Earth’s entire energy consumption. Accelerating to 80% could required 100% of 2013’s energy consumption. Now consider that to colonize the universe, we need to send upwards of 100 million (10^8) probes.
Since we need to both accelerate and decelerate a probe, this energy is required twice over. Doubling the mass of the probe doubles the energy required, but doubling the target speed multiplies the energy required many times over even at very small fractions of the speed of light.