glsp c* Final mass Propellant mass
Final mass T
Isp =-= Thrust produced per unit mass flow rate of propellant
So we have just two key parameters: the weight ratio, or mass ratio, is just a measure of how much propellant is carried. The characteristic velocity, or the specific impulse, Isp, defines the performance of the propulsion system. The best cryogenic chemical rockets today have an Isp of 460 s (4,462m/s). That means that a mass flow of one kilogram per second generates 460 kilograms (4,462 newtons) of thrust. If our benchmark change of speed AV is the speed of light (299,790,000 m/s) then the specific impulse required for a mass ratio of 6 is 17,062,060 s. That is, one kilogram per second of propellant flow generates 17,062,060 kilograms of thrust. Or more pointedly, one microgram per second of propellant produces 17.06 kilograms of thrust! That is approaching a so-called "massless" thrust-producing system, and is well beyond our current concept of generating thrust. Even if at some future time an Isp of 100,000 s is achieved, the speed of light (299,790,000 m/s) is 170 times faster the incremental velocity provided by a mass ratio of six.
If our benchmark distance is one light-year, or 5,880 billion (5,880 x 109) statute miles, or 1,602 times more distant than Pluto, to reach that distance in a 15-year oneway time the specific impulse of the propulsion system would have to be 1,602 times greater than that of current rockets. If that was so, we could travel 1,602 times farther in the same 15-year time period. That is, the propulsion system Isp must be 1,602 times 300 s (the best Isp feasible with storable propellants), or 480,600 s, or a characteristic velocity of 4,713,000 m/s, about 1.6% of the light speed. The most advanced nuclear electric propulsion we have today is capable of about 4,000 s, just 13.3 times greater than current storable propellant rocket specific impulse, so that we can travel 13.3 times farther in the same 15-year time period, or 48.8 billion statute miles. This enables us to reach the so-called "Oort Cloud'', the origin of long-period comets, and a region of space very distant from any major astronomical object outside of our Solar System. So we are confined to our Solar System if our travel time is going to be the duration of a human project team and our current propulsion systems. At the distance of one light-year and with current storable propellants, the travel time to one light-year distance from Earth is about 24,032 years. That is about the length of human recorded history. With our best nuclear electric propulsion the time to one light-year distance is 1,807 years.
Within our Galaxy, to reach a-Centauri (or: Alpha Centauri), one of the seven stars within 10 light-years of Earth and 6,580 times more distant than Pluto. In 15 years' one-way travel, the specific impulse would have to be over 1.970 x 107 s, or the characteristic velocity 64% of light speed. If we could develop a propulsion system with an exhaust velocity equal to the speed of light, the specific impulse would be 30,569,962 s. Our Galaxy is a spiral galaxy about 100,000 light-years in diameter with a central "bulge" about 20,000 light-years deep. Our Solar System is about 33,000 light-years from the galactic center. To reach past our Galaxy to our nearest galaxy, Andromeda, that is 3,158,000 times more distant than Pluto, the Isp would have to be on the order of 950 x 109 s and the characteristic velocity would have to be an impossible 6.47 x 1012 or 21,600 times the light speed. That velocity is not conceivable within our current understanding of physics. Figure 1 shows the spiral galaxy Andromeda in ultraviolet wavelength by the GALEX Satellite and in visible light (see the GALEX/JPL website). The Andromeda Galaxy is the most massive of the
local group of galaxies, which includes our Milky Way, and is the nearest large galaxy similar to our own. The GALEX ultraviolet image shows regions of young hot, high-mass stars tracing out the spiral arms where star formation is occurring. The central white "bulge" is populated by old and cooler stars formed long ago, and where a central supermassive black hole is very likely located. The GALEX image is compared to a visible light image. The stars in the foreground are stars in our Galaxy, the Milky Way. The composite image from the JPL website in Figure 2 reveals a star-forming region at the center of the Milky Way as recorded by several infrared wavelengths invisible to the eye [irastro.jpl.nasa.gov/GalCen, 2005]. A black hole three million times heavier than our Sun has a gravitational pull so powerful that not even light can escape from its surface. The dusty material (called the Northern Arm) in the picture is spiraling into the black hole, and may trigger the formation of new stars. The black hole continues to grow larger as this material falls into it. The small bright star just above the black hole and to the left of the larger star is a red super giant nearing the last stages of its life. It is 100,000 times brighter than our Sun. The scale of the MIRLIN (Mid-Infrared Large Well Imager) is indicated by the one light year bar
Related to this aspect of travel is the chance of discovering life, perhaps intelligent life, that has been the underlying purpose of all human exploration since Homo erectus started wandering and eventually moved out of Africa. Life as we know it at least, may exist only under a narrow band of planetary conditions: for instance, a life-hosting planet must orbit a star or stars not too hot or too cold, must be of the right density, and so on [Gonzalez et al., 2001]. Figure 3, from Scientific American, shows the Galactic habitable zone and the Solar habitable zone. To the center of our
1.0 light year
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