**7. Theoretical speeds**

It is possible to theorize the speeds capable of being achieved by matter/antimatter-propelled spacecraft, based upon some reasonable assumptions involving the mass of the spacecraft and the production of paired particles by the system.

*Matter/Anti-Matter Propulsion DOI:http://dx.doi.org/10.5772/intechopen.110310*


$$F = ma \left( \text{Newton's Second Law} \right) \tag{2}$$

and

$$
\mathfrak{a} = \mathcal{F} \nmid \mathfrak{m}, \tag{3}
$$

The spacecraft will accelerate at approximately 1.9 m/s/s.

4.The formula for the velocity achieved by a constantly-accelerating object, starting at rest, is

$$
\boldsymbol{w}\_f = \boldsymbol{a}\mathbf{t},\tag{4}
$$

where, for our purposes, by international convention, velocity (final) is measured in meters/second (direction is not relevant for this purpose), acceleration is measured by meters/second/second, and time is measured in seconds.

5.Because there are 31,536,000 seconds in a year, the speed achieved by the spacecraft hypothesized here, after 1 year, would be approximately 6 × 107 m/s. Because the speed of light (*c*) is approximately 3 × 108 m/s, the spacecraft would, after 1 year, be traveling at approximately 20% of the speed of light. After 2 years of constant acceleration, the spacecraft would be traveling at approximately 40% of the speed of light.

Mission planning would necessitate sufficient time for deceleration, but these speeds, if achievable, indicate that relativistic speeds—speeds even approaching the speed of light—are conceivable with matter/anti-matter propulsion.
