Relativity Lite

34 | Relativity Lite additional 2 × 1.456 = 2.912 years to add to the saucer’s 11.648 years to give 14.56 years . That is, the Earth has sent 10 pulses, one at the end of every 1.456 years , for a total of 14.56 years , with the final one not shown, since the saucer has come to rest at the time it would normally have been emitted. All three methods are consistent. SAUCER FRAME We turn now to the saucer frame of reference in which the saucer is at rest and the Sun and Alpha Centauri move off to the left for almost six years and then move back to the right to return the Earth to the saucer’s position. Note that in figure 11, the distance between these two stars is now about 3.5 of the 1 c year grid spacings. Indeed, if we apply length contraction to the moving pair of stars, the distance from the Sun to Alpha Centauri should contract to = = = L c yr c yr γ 4 37 1 25 3 49 . . . . So we would expect a travel time of τ = = = L v c yr c yr 3 6 5 827 .496 . . each way, or 11.648 years total. If you are running RelLab, set the clock to zero in the file “Alpha Centauri Trip 3c 10Eflash” and set “Frame: Saucer 1” in the upper left-hand corner. Figure 11. The distance between the Sun and Alpha Centauri is contracted to 3.49 light-years in the saucer rest frame. The grid lines are 1 c year apart. We have moved the two stars somewhat to the right on the screen in order to accommodate their leftward motion as they move away from the still saucer. Figure 12. At 1.6 years into the trip, showing the emission of the first ( red ) saucer pulse expanding about two months after it was emitted at the agreed-­ upon time of 1.456 years .