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Which gives a property of the rotation or transformation matrix MTM 1. The transpose of a matrix interchanges the rows and columns by Mj Mji. It is then possible to use this information to find the entries of the matrix M. The unchanged length of a vector under this transformation, called its invariance, means that the components of V and V' are ct, x, ,y, z and ct', x', y', z' respectively with -(ct')2 + (x')2 + (y')2 + (z')2 -(ct)2 + x2 + y2 + z2. (6.5) This problem is simplified by...

R n 1F814

The angle of the radial vector along the lens would be 0 2 r R. which for n 1.5 it is easily found this lens will have a thickness of 60 m. Obviously this is not practical due to the huge mass of such a lens. However, a Fresnel lens will work. The material set into concentric Fresnel zones which act as a slice of the lens at some radius. The sum of these over all concentric zones will concentrate light in the same fashion that a single lens does 8.2 . This technique is used...

Will Humans go to the Stars

It is common for science fiction novels and screenplays to portray starships manned by people, often a rather large number of people. This of course goes back to Jules Verne, where space was seen as something to be explored by people. In the early days of the Soviet and American space programs considerable interest was put forth in piloted spacecraft. The so called race to space was seen as a contest over which side could put astronauts on the moon. It echoed the science fiction screenplays of...

Elements of Astrodynamics

Even if one has the propulsion and power technology to send spacecraft into space this is not enough. To send a spacecraft to the moon one does not just point the rocket at the moon like a rifle pointed at a target. A spacecraft travelling anywhere in the solar system is influenced the gravity field of nearby planets and the sun. Thus the trajectory of a spacecraft is not going to be a straight line. This is most clearly the case for a satellite orbiting the Earth. So for these Newtonian...

Exotic Propulsion Methods

Wormhall Svg

All afficianados of science fiction are familiar with warp drives, wormholes, transporter beams and other exotic methods. They permit the scripting of a science fiction screenplay without the complexities of relativity and as a way around the light speed barrier. These ideas are not completely without some connection to physics, but the connection is very long and probably thin to the point of being nonexistent. Yet if a warp drive could be developed a spacecraft could travel to another star...

The Interstellar Neighborhood

This chapter discusses possible destinations for low gamma spacecraft. There are a number of G-class stars accessible to low gamma spacecraft. These might have terrestrial planets worth exploration. Most of the nearby stars are M-class red dwarf stars. It is unlikely that biologically active planets exist around these stars. However, since they make up the largest number of stars in the galaxy they are still systems worth a close examination, possibly by a starcraft. The stars within 10 light...

Electromagnetically Accelerated Nanobots

Electromagnetic Rail

A hot topic in advanced technology in these early days of the 21st century is nanotechnology. While the future trajectory of this technology is very uncertain, it is worth writing a short chapter on the prospect for the use of these as interstellar probes. Nanotechnology is the engineering of systems on the molecular or near molecular scale. These systems are computers with an instruction set encoded on molecules, in a way similar to what nature provides with DNA. These instructions are then...

The Relativistic Rocket

The most reaching proposed method of propulsion, project Daedalus, can in principle send a spacecraft to at best about 10 the speed of light. It is clear that something more robust is required to explore a star system, particularly if it is more than 10 light years from our solar system. The specific impulse required to reach a significant percentage of the speed of light must be close to the speed of light divided by one-gee. The ideal case would be for s c g 3 x 107 sec. In this case the...