Below is a table that compares gammas with the fraction Eph/mc?

Y |
Eph/mc | ||||||||||||||||||||||||||||||||||||||||||||

1.5 |
0.559 | ||||||||||||||||||||||||||||||||||||||||||||

1.6 |
0.624 | ||||||||||||||||||||||||||||||||||||||||||||

1.7 |
0.687 | ||||||||||||||||||||||||||||||||||||||||||||

1.8 |
0 . 748 | ||||||||||||||||||||||||||||||||||||||||||||

1.9 |
0 . 808 | ||||||||||||||||||||||||||||||||||||||||||||

2.0 |
Equations 8.5 and 8.6 indicate the need to reflect a lot of photons! Assume that this sail craft is powered by some solar collector near Earth. If the collector is near Earth there are about 1500 watts/m2 of power of solar radiation. For a year as ~ 3 x 107 sec a meter would collect 4.5 x 1010 J. So the mc2 equivalent is about 5 x 10"7 kg. So collecting area is important. To reach a 7 = 2 in one year requires an area of around 1.7 x 106 m2 to accelerate 1 kg to this speed. The collector would require a radius of 525 meters, where this assume 100% conversion of solar light energy to a beam that drives the spacecraft. Clearly for a larger spacecraft the area goes up proportionately. For the 107 kg craft mentioned above this would imply a light collecting area with a ~ 1500 km radius. The photon sail offers the advantage of not requiring exotic engineering and physics. It also clearly has potential performance capabilities of the photon rocket. However, it requires the construction of large solar collectors. Clearly as this photon sail clears the solar system it will have to be driven forward by a directed beam of light energy. This will require some sort of solar concentrator or a solar driven laser beam of truly huge proportions. A 500 m radius collector receives 2.35 gigawatts of power, where in reality the conversion losses will require a ~ 1600 m radius collector. Hence the scale of things becomes colossal and requires large scale fabrication in space. An examination of the times and distances required to accelerate to a 7 = 1.15, or v ~ .5c, for an average acceleration g = .01 m/sec2 to g = .1 m/sec2 g (m/s2) 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 257.7 171.8 128.8 103.1 t (yr) 540.85 270.4 180.3 135.2 108.17 90.14 77.26 67.61 60.09 54.08 17.86 15.87 14.29 The time and distance performance is not very good, but a solar sail with the higher end of these specification may well be able to reach some of the nearer stars within a 5-10 ly distance. This performance might be improved if the light is further concentrated. Assume that the average accelerations are increased by a factor of 2.5. The performance is then
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