# Star Missions

My characters in Robot Dawn do not travel to other stars; however, the Feds and Uni-Feds do have a joint project with robotic spacecraft traveling to the closest stars, Alpha Centaur and Barnard’s Star, and they are there during the timespan of the novel. In Robot Dawn, one of the more interesting scenes occurs at SE-L4. (To learn about Lagrange Points, click here.) Daisy’s father is taking over the directorship of the Deep Space Observatory at SE-L4. Several scientific projects are located there, the most interesting of which is the reception of data from the missions to Alpha Centauri and Barnard’s Star. These missions have capitalized on the practically infinite supply of power in the form of Cold Fusion and the thrust-without-propellant EmDrive. They provide constant  and continuous one-g acceleration to the spacecraft going to the Alpha Centauri trio of stars and also Barnard’s Star. Since one-g acceleration for one year yields a velocity approaching the speed of light, we must use Einstein’s Theory of Relativity to determine how long it will take the spacecraft to get to their destinations. (Remember that nothing can travel faster than the speed of light.) Thankfully, that has been accomplished and the equations presented online by Philip Gibbs of the University of California – Riverside in an article (1996) titled The Relativistic Rocket. Gibbs analysis leads to the following equations:

t = = sqrt[(d/c)^2 + 2d/a]     Eq (1)

d = (c^2/a) (sqrt[1 + (at/c)^2] − 1)    Eq (2)

v = at/sqrt[1 + (at/c)^2]    Eq (3)

Where:
t = time from launch
d = spacecraft distance from Earth
v = spacecraft velocity relative to Earth
c = speed of light
a = spacecraft acceleration – assumed constant

In equation (1), since “a” and “c” are constants, we can select a range of values for “d” and compute the corresponding time for each distance.  See the figure below, which was created in Matlab. The acceleration used is 9.81 m/sec^2, which is that acceleration of Earth’s gravity that we call one-g. The bottom orange curve is for constant acceleration of one-g all the way to the star, and we zoom on past. The blue line is for acceleration halfway and deceleration during the second half, so that we end up at the star rather than doing a flyby. The time in each case is indicated by the vertical lines. The Alpha Centauri trio of stars are all at about 4.3 lightyears, and Barnard’s Star is at about 6.0 lightyears from Earth. (Remember that a lightyear is the distance light travels in a year and not a time period.) What the two curves show is that the time to the stars is not that different when accelerating/decelerating to stop at the star when compared to the time to get there with constant acceleration all the way. This is because the spacecraft approaches the speed of light at the end of the first year and cannot go much faster even though accelerating at one-g the rest of the time.

In the novel, the spacecraft to the trio of stars called Alpha Centauri arrives at about the same time as that to Barnard’s Star. This is because the spacecraft to Alpha Centauri was launched after those to Barnard’s Star. In both cases, the spacecraft stop at the stars to investigate the planets about those stars in what is called the “Goldilocks Zone,” where it is possible for life as we know it to have evolved.