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                        A new propulsion technique has been dis-
                  covered which  allows  manned  missions to ANY
                  planet in the solar  system.  Travel time will
                  vary from 5 weeks to Mars to  6 months for the
                  outer planets(radiation hazards prevent visits
                  to Mercury or Venus).  This technique  employs
                  a form of propulsion where  momentum is trans-
                  ferred  from "smart" projectiles to the space-
                  ship by catching the projectiles with an EMPL.
                  The projectiles  would be thrown  from another
                  EMPL located  at the  north  pole of the Moon.
                  Both  EMPLs would be driven by  nuclear power.
                  The specific impulse of the system, which will
                  be 3400 seconds initially, can be increased to
                  any desired value by increasing the power.
                        With this propulsion system we can visit
                  all the other planets within our own lifetime!
                  It is envisioned that the full scheme will re-
                  quire  30 years to implement.  The  spaceships
                  will be reusable, so the one which takes us to
                  Mars can also take us to Jupiter and Saturn.


                Momentum transfer can be used as a propulsion system to
           move  heavy  spaceships  between  Earth and ANY of the other
           planets  at  much  higher  speeds than can be attained using
           other current methods of propulsion. This scheme,in contrast
           to  other  momentum transfer schemes such as those suggested
           by  G.K.  O'Neill  or C.E. Singer, permits fast manned round
           trip missions.
                Many authors have suggested using EMPLs to throw things
           into space either from Earth or from the moon. Only a few of
           these  authors have suggested that their schemes amounted to
           spaceship  propulsion systems. Among those who have are G.K.
           O'Neill and C.E. Singer.
                 In  his 1977 book, "The High Frontier", Gerald O'Neill
           described  what  he  called  a "reaction engine". This was a
           mass-driver which  used electromagnetic fields to accelerate
           buckets  filled  with surplus mass which would be thrown out
           into  space  [p.141].  This would then  accelerate the mass-
           driver  and whatever  it  was  attached  to  in the opposite
           direction according to Newton's third law of motion. O'Neill
           suggested  that  such a reaction engine could be attached to
           an  asteroid  and  could  push the asteroid back to Earth by
           chewing  up  part  of  the  asteroid and spitting it out the
           back.  Of  course, he conveniently forgot to tell us how the
           reaction  engine  would get from here (or the moon or L5) to
           the asteroid in question.
                 Although  O'Neill's  scheme  uses  an EMPL to move the
           asteroid  or  spaceship,  it still requires the huge onboard
           reaction mass which must be thrown away to move the ship. It
           is  clear that this method will not work efficiently to move
           people  from one planet to another. For example, in order to
           go  from  the  moon to Mars, you would have to lift reaction
           mass  from  the  moon to the ship just so you could throw it
           away  from  the ship to push you toward Mars. You would have
           to  carry a lot of extra material to throw away when you got
           to  Mars  in  order to enter a stable orbit around Mars. The
           only  advantage  of  this  scheme over a conventional rocket
           departure  from  Earth is that the reaction mass coming from
           the  moon  would be much cheaper than rocket fuel that would
           have to be lifted from Earth.
                 In  1979,  Clifford  E.  Singer  proposed  a  momentum
           transfer scheme which used a stream of high velocity pellets
           weighing  only  about 3 grams each to propel an interstellar
           probe.  The  idea  was  to  use a very long EMPL deployed in
           interplanetary  space  to  accelerate the tiny pellets. They
           would  impact the starship and transfer their momentum to it
           thus  accelerating  it  to  very high (0.12 c) velocity. The
           specifications  of  Singer's  scheme are given in the center
           column of Table 1, below. Apart from the ludicrous nature of
           his plan, it suffers from several fatal deficiencies.
                 The  Singer  proposal  fails  for all of the following

           1.  Any pellet which hits the spaceship will destroy it.
               The energy of a 2.8 gram pellet moving at 0.25 c is
               about 7.875e+12 joules which is equivalent to 1.884
               kilotons of TNT (i.e. a 2 kiloton atomic bomb).
           2.  The spaceship can't carry enough fuel to adjust its
               position to enable it to catch pellets which are out
               of alignment.
           3.  The spaceship can't carry enough electric power
               generating capacity to generate a magnetic field
               strong enough to stop the pellets. The mass of a 15,000
               gigawatt generator would be at least 3,000,000 MT at
               0.2 MT/MW.
           4.  The pellet dispersion due to the influence of Jupiter,
               Saturn, Uranus, Neptune, the Oort cloud, other objects,
               and unknown interstellar dark matter would cause many
               pellets to miss the ship or to collide with the electro-
               magnet (of 3.) if one existed.

           The Singer proposal is useless for humans because:

           1.  It is not intended for interplanetary travel.
           2.  It is not capable of round-trip missions.

           The Singer proposal is highly impractical for at least
           the following several reasons.

           1.  Here on Earth it takes us years to build a bridge just
               a couple of kilometers long.  How long would it take to
               build a facility in the orbit of Jupiter which would be
               100,000 kilometers long?
           2.  How much would such a facility cost?  Who would want
               to pay for it?  Certainly no taxpayers I know!
           3.  Who would want such a facility that wasn't capable of
               launching manned missions?
           4.  The real-world engineering problems are simply
           5.  Vastly superior methods for launching of interstellar
               probes exist - such as: matter - antimatter propulsion
               or the Daedalus project of the British Interplanetary


                For years space scientists the world over have sought a
           propulsion system which could  significantly reduce the time
           needed  for  interplanetary travel. My colleague, Albert Wu,
           and  I have discovered such a propulsion system. This scheme
           works  by  transferring  momentum  from  a series of "smart"
           projectiles (launched from an EMPL located at the north pole
           of  the  moon)  to the spaceship by catching the projectiles
           with another EMPL on board the spaceship. A spaceship with a
           crew  of 1000 can now travel to Mars in under two months and
           to Jupiter in six.
                The prime mover is nuclear power which converts mass to
           energy  according  to  Einstein's  equation  and  drives the
           EMPL's  which  launch  the projectiles. As these fast moving
           projectiles  are  caught  by  the  spaceship's  EMPL,  their
           momentum  will  be transferred to the spaceship according to
           Newton's  third law of motion. This reaction will accelerate
           the  spaceship  in  the  desired  direction  by  an   amount
           proportional  to  the ratio of the mass of the projectile to
           the mass of the spaceship. As each projectile is caught, the
           combined  mass  will  be  increased  by  the  mass  of   one
           projectile.  This  means  that  some  of  the  momentum   of
           subsequent  projectiles  will  be used to accelerate projec-
           tiles  that have already been caught. That energy is wasted.
           For that reason, the projectiles will be launched toward the
           spaceship  in groups - each projectile separated by the time
           and  distance required by the EMPL on board the spaceship to
           charge  up its capacitors to catch the next projectile. Once
           the  spaceship  has  caught  all  of  the projectiles in one
           group, it will proceed to launch them again in the direction
           opposite to the desired trajectory of the spaceship. In this
           manner  each  projectile  will  contribute two small accele-
           ration pulses to the spaceship.
                 Since the moon is locked in its orbit about the Earth,
           the  same  part  of  the moon always faces Earth. This means
           that  as  the  moon rotates there are only two points on its
           surface  from which an observer should be able to constantly
           observe  the Sun (ignoring the moon's inclination) - namely,
           the  north  and  south poles. Due to the fact that there are
           few  maria  in  southern  lunar  regions (and for other good
           reasons)  the  north  pole has been selected for the site of
           the  lunar  EMPL. The capacitor driven EMPL will be about 10
           kilometers  long and will be capable of launching one metric
           ton  projectiles  at  velocities  of up to 20 kilometers per
           second.  This will require something on the order of 200,000
           MJ  of  energy for each launch - which will be supplied by a
           2500 MW nuclear power system. The reactor will require about
           two  minutes  to charge the capacitors between the launching
           of each projectile. The launcher itself will be mounted on a
           series of circular tracks, so that it can be rotated between
           each  launch  to  compensate  for the orbital motions of the
           Earth  and  the moon. The Earth orbits the Sun in a prograde
           direction  at  about 29.8 kilometers per second and the moon
           orbits  the Earth also in a prograde direction at about 1.02
           kilometers  per second. Thus for launches two minutes apart,
           the launcher would be rotated in the retrograde direction by
           5  to  10  meters  depending  on  the  final velocity of the
                 In  order  to  accelerate  the  spaceship  to cruising
           velocity  it  will  be  necessary  to throw several thousand
           projectiles from the moon to the spaceship (assuming none is
           reused).  Since each individual projectile will be separated
           by  about  two minutes and each group by several hours, this
           process  will  take  several days. Thus the moon will rotate
           significantly  during  the  launching  of  the projectiles -
           perhaps  as much as 45 degrees. The tilt of the orbital axis
           of  the  moon relative to a normal to the ecliptic plane may
           prevent  launching  of projectiles during part of the moon's
           orbit,  but this will be only a small percentage of the time
           and will not interfere with our plans.
                 The spaceship itself will have three major components:
           an  electromagnetic  projectile  launcher/catcher, a nuclear
           power  system  to  provide the electricity to drive the EMPL
           (and  everything  else), and the crew's quarters. The entire
           spaceship will be rotated axially about the long axis of the
           EMPL  to  provide  gyroscopic  stabilization  and artificial
           gravity  for  the  crew.  In  order  to  make the artificial
           gravity  relatively  uniform,  the  crew's  quarters will be
           constructed  in the shape of a ring. The ship's EMPL will be
           about  6  kilometers  long  and  the  on board nuclear power
           system  will  be  rated  at about 500 MW. These capabilities
           should allow the spaceship to launch or catch one metric ton
           projectiles at up to 10 kilometers per second at roughly two
           minute  intervals. Of course it could handle higher velocity
           projectiles at the cost of longer  capacitor charging times.
                 The  anticipated  mass  of  the spaceship will be 3000
           metric  tons.  This  includes  1900  tons  for the EMPL (317
           kg/meter), 100 metric tons for the nuclear power system (0.2
           MT/MW),  and  1  metric  ton per crew member for each of the
           1000  crew  members. The allocation per crew member includes
           everything:  the  crew  member, his clothes, his space suit,
           his  furniture,  his  food production facilities, his equip-
           ment, his living quarters, air, water, and so on.
                 Food will be grown on board in a hydroponic production
           facility.  Each of these goals will be difficult to achieve,
           but  ingenuity  and perseverance will triumph. Some latitude
           is also possible - i.e. 4000 tons would be manageable.
                Due to the artificial gravity, the crew will be able to
           move  about  relatively  normally - to eat, to sleep, and to
           accomplish  simple  bodily  functions normally. In addition,
           human  muscles  should  not  atrophy  and  extensive   daily
           exercise  programs  will  not  be  necessary.  Perhaps  most
           importantly,  the artificial gravity should be sufficient to
           inhibit the bones of the crew from decalcifying - a known and
           very dangerous consequence of weightlessness.
                 There  are numerous reasons for carrying a large crew.
           Among them are the following:

           1. It will transform the first Mars mission into the
              greatest international expedition of all time.
           2. It will cause an exponential increase in public
              interest and political support for the project.
           3. Actual participation, in the form of on board seats,
              can be sold to the public worldwide to raise funds
              to support the project.
           4. The cost per person will be greatly reduced from
              that which would occur if a crew of fewer than 10
              were sent on a similar mission.
           5. The knowledge and experience to be gained from a
              large crew is clearly much greater than could be
              accomplished with a small crew.
           6. The crew will not be a small elite group selected
              in some obscure suspicious way by unknown and
              untouchable bureaucrats.
           7. Crew members need not be special in any way (except
              perhaps in not being seriously ill); however, since
              weight will be important, women may have a preference.


                The first expedition to Mars can be sketched out in the
           following paragraphs. Using materials derived from the moon,
           a  10  kilometer EMPL will be built at the north pole of the
           moon.  From there it will be possible to launch objects into
           the  plane  of  the  orbit  of the moon and to either of the
           Lagrangian  points,  L4 or L5. Again using materials derived
           from the moon, a spaceship will be assembled in orbit around
           the  Earth  at  L4 or L5. This will be an unmanned spaceship
           consisting  primarily  of  a  6  kilometer EMPL and a 500 MW
           nuclear  power  system to drive it. The fissionable material
           for  the  nuclear  power system will be supplied from Earth.
           This  spaceship  will  carry  a  cargo  of  several thousand
           "smart"  projectiles, which will be produced on the moon and
           lifted  to  the spaceship. The ship will break away from the
           Earth's  gravity  by  launching a few hundred of the projec-
           tiles  in  the opposite direction. Next, the Lunar EMPL will
           launch  more projectiles toward the spaceship. These will be
           caught  and saved by the spaceship, but they will accelerate
           the  ship on its way to Mars. After a leisurely trip it will
           approach  Mars.  By launching several hundred of its projec-
           tiles,  the  ship  will  enter  a circular orbit about Mars.
           There  it  will  locate  and  match  orbits with Phobos, the
           larger  satellite  of  Mars.  It  will then attach itself to
           Phobos and await the arrival of the next (manned) spaceship.
                 The  second  spaceship  will be assembled in a similar
           manner  at L4 or L5. But this ship will have a crew of 1000,
           who  will  be lifted from Earth by one of the various ground
           to  space  planes currently being developed such as Hotol or
           Spacebus  or  Space  Van  or the German Sanger project. They
           will  be  lifted  from the Freedom space station (or Mir, if
           Freedom is cancelled) to L4 or L5 with the same space plane.
                A few hundred projectiles will also be carried on board
           the spaceship. They will be used to break out of Earth orbit
           as  the first ship did. Once on its way, the Lunar EMPL will
           begin  launching groups of projectiles toward the spaceship.
           It  will  require  about  160  projectiles  to  increase the
           velocity  of the ship by one kilometer per second. After the
           ship  catches  and relaunches 20 groups, the ship's velocity
           will  be  about  19  kilometers per second. Cruising time to
           Mars  will  be  about 41 days. When the second ship is still
           several  days  from Mars, the first ship will launch projec-
           tiles  to  slow  down  the  second  ship.  It  will  then be
           maneuvered  into  orbit  around Mars. Actual landing on Mars
           and  return  to  Martian orbit will be accomplished with the
           usual LOX-LH2 produced from water present on Phobos.
                 The  return  trip  will  be  similar,  beginning  with
           breakaway  from  Martian  orbit  and  the  launching of more
           groups  of  projectiles  from the EMPL now on Phobos. As the
           returning  ship  approaches  the  moon,  projectiles will be
           launched  from the Lunar EMPL to slow down the ship and help
           maneuver it into high Earth orbit again.
                 Note  that  Phobos has a very low gravitional field so
           that  the first ship will be able to attach itself to Phobos
           without  damage.  (This  may require partial disassembly and
           re-assembly of the EMPL.) Conversely, Phobos is large enough
           that  the  launching  of several thousand (or even millions)
           projectiles will not disturb its orbit.


                The following table compares the  specifications of the
           C.E. Singer proposal with those of this scheme.

                                   Table 1

                                   C.E. Singer      C.R. Willis
           EMPL length             100,000 km       10 km
           EMPL power requirement  15,000 GW        2,500 - 40,000 MW
           EMPL deployment         interplanetary   north pole of moon
                                   space            & onboard spaceship
           Projectile mass         3-100 gms        1-3 MT
           Projectile velocity     0.25 c           10 - 300 km/sec
           Projectile guidance     none             complex
           Projectile acceleration (0.3 - 4)e+6 g   (0.5 - 20)e+3 g

           Spaceship mass          under 1000 MT    3000 - 5000 MT
           Spaceship velocity      0.12 c           10 - 300 km/sec
           Spaceship crew          none             1000

           ( EMPL = Electromagnetic projectile launcher )


               The total delta velocity of the outward bound leg of the
           Mars mission is about 40,000 meters per second or 40 km/sec.
           This corresponds to a  mass ratio of about 5393 for a rocket
           using LOX-LH2 for fuel and having a specific  impulse of 475
           seconds. For a nuclear thermal rocket with  specific impulse
           of 950  seconds it  corresponds to a mass ratio of about 73.
           For a specific impulse of 2000 seconds the mass ratio = 7.4.
           However, since the fuel, i.e. the  projectiles, are not car-
           ried on board, the (fuel) mass is about 7000 MT.  This gives
           a mass ratio of about 3.33 (10000/3000) which corresponds to
           a specific impulse of about 3390 seconds. Thus the effective
           specific impulse is much  higher  than  the exhaust velocity
           divided by 9.8.
                This scheme offers readily attainable specific impulses
           in  the  range  of  2000  to  10,000  seconds - or spaceship
           velocities of 20 to 100 km/sec. But, best of all it requires
           carrying almost no fuel!  Small amounts of fuel will be car-
           ried for limited  maneuvers.  What is the  primary tradeoff?
           The faster you want to go, the  more nuclear  power you need
           to drive the EMPLs. How much?


                                     Table 2
                                  Mars mission:
           Launch      Lunar polar EMPL    Relative    Spaceship's EMPL
           velocity      (10 km long)      velocity       (6 km long)
           20 km/s         2500 MW          10 km/s          500 MW
                                Jupiter mission:
           Launch      Lunar polar EMPL    Relative    Spaceship's EMPL
           velocity      (10 km long)      velocity       (6 km long)
           40 km/s        10000 MW          20 km/s         2000 MW
                                 Saturn mission:
           Launch      Lunar polar EMPL    Relative    Spaceship's EMPL
           velocity      (10 km long)      velocity       (6 km long)
           80 km/s        40000 MW          40 km/s         8000 MW


                 Now  let  us  look  at  missions to Mars, Jupiter, and
           Saturn. The velocity to Mars will be 20 km/sec, the velocity
           to  Jupiter  will  be  40 km/sec, and the velocity to Saturn
           will  be 80 km/sec. The following table was prepared to show
           sample  departure dates and arrival times. Note that 'Travel
           time' is ROUND trip. One way is about half. All times are in
           Earth days.

                                     Table 3

                 Missions to Mars: outward velocity = 20 km/sec
                 Outbound            Inbound        Travel+Mars  =Total
              Depart   Arrive     Depart   Arrive    time  time   trip
            6/ 3.2/01  7/11.0   8/15.3/03  9/17.9   71.35+765.30=836.65
            8/22.2/03  9/24.4  10/22.3/05 12/ 2.0   74.08+758.78=832.86
           10/28.7/05 12/14.2  12/ 3.9/07  1/24.4   97.91+719.74=817.65
           12/11.2/07  2/ 7.7   1/ 5.1/10  3/ 4.7  117.14+697.39=814.53
            1/13.6/10  3/17.5   2/ 6.8/12  4/ 7.8  123.95+691.27=815.22
            2/16.0/12  4/16.7   3/14.9/14  5/11.6  118.41+697.21=815.62
            3/24.3/14  5/16.7   5/ 1.9/16  6/18.9  101.35+716.28=817.62
            5/10.1/16  6/21.5   7/12.7/18  8/17.1   77.82+751.16=828.97
            7/19.4/18  8/21.2   9/29.3/20 11/ 5.1   69.56+770.10=839.66
           10/ 5.9/20 11/15.2  11/19.0/22  1/ 5.6   87.89+733.82=821.71

                 Missions to Jupiter: outward velocity = 40 km/sec
                 Outbound            Inbound       Travel+Jupiter=Total
              Depart   Arrive     Depart   Arrive    time  time    trip
           11/ 9.8/00  5/24.4   8/24.6/01  3/ 9.6  392.67+ 92.13=484.79
           12/13.1/01  7/ 4.7   9/19.5/02  4/10.9  407.02+ 76.78=483.80
            1/13.6/03  8/11.8  10/15.3/03  5/11.1  419.01+ 64.49=483.50
            2/12.9/04  9/13.7  11/11.7/04  6/11.1  425.23+ 58.97=484.20
            3/14.4/05 10/13.6  12/13.3/05  7/12.2  424.11+ 60.70=484.81
            4/14.6/06 11/ 9.5   1/19.3/07  8/14.4  415.99+ 70.76=486.74
            5/17.6/07 12/ 5.6   2/28.3/08  9/16.1  402.97+ 84.50=487.47
            6/20.7/08  1/ 1.2   4/10.9/09 10/22.4  388.87+ 99.78=488.65
            7/27.8/09  2/ 1.4   5/22.2/10 11/28.1  378.46+109.83=488.29
            9/ 3.8/10  3/ 9.6   6/29.5/11  1/ 4.5  375.79+111.90=487.69

                 Missions to Saturn: outward velocity = 80 km/sec
                 Outbound            Inbound        Travel+Saturn=Total
              Depart   Arrive     Depart   Arrive    time  time   trip
            3/11.9/10  9/19.6  11/ 8.7/10  5/19.6  383.29+ 50.09=433.38
            3/24.8/11 10/ 5.1  11/19.7/11  5/31.7  388.32+ 45.57=433.89
            4/ 5.6/12 10/19.2  11/29.0/12  6/13.4  393.02+ 40.82=433.84
            4/18.2/13 11/ 2.3  12/ 9.6/13  6/26.1  397.19+ 36.74=433.93
            4/30.6/14 11/17.0  12/20.7/14  7/ 8.9  400.67+ 33.70=434.37
            5/12.8/15 11/30.5  12/31.6/15  7/20.2  403.33+ 31.04=434.36
            5/24.3/16 12/12.6   1/11.2/17  8/ 1.7  405.06+ 29.58=434.65
            6/ 5.2/17 12/25.1   1/22.8/18  8/13.8  405.82+ 28.78=434.60
            6/17.3/18  1/ 6.0   2/ 4.4/19  8/26.2  405.57+ 29.35=434.92
            6/29.5/19  1/17.6   2/17.8/20  9/ 7.1  404.32+ 31.24=435.56


                 What  are  the  advantages  of this scheme compared to
           current spaceship propulsion systems?

           1. Crew safety.  Due to the provision of artificial gravity,
              which is in turn  due to the large size of the spaceship,
              the  crew will  experience normal  gravity throughout the
              trip rather than  the very dangerous  microgravity of all
              past or currently planned missions.
           2. Crew size. Due to the very large crew (of 1000), the per-
              sonnel  will  not be a small elite group selected in some
              obscure and suspicious way  by  unknown  and  untouchable
              bureaucrats.  Ordinary  people will be able to buy a seat
              or seats.
           3. Crew  comfort.  Due to  the large size  of the spaceship,
              each  crew  member  will enjoy  75 cubic meters of living
              space.  Crew members will be invited to help design their
              own quarters.
           4. Short trip  duration.  The  momentum transfer  propulsion
              system can  transport the  spaceship to Mars in as little
              as 35 days or 5 weeks (assuming a velocity of 20 km/sec).
              As  can  be  seen  from  table 3 above, the trip duration
              varies from about  35 days to about 62 days, depending on
              the date  of departure.  The current  Mars  Observer will
              take 337 days to fly to Mars.
           5. Reusability.  The spaceship  will be  reusable because it
              will  be  assembled in free space and will  never land at
              any of its  destinations.  This means  that the spaceship
              which we take  to  Mars  can  also take us to Jupiter and
              then to Saturn, or it could become a shuttle simply going
              back and forth between lunar orbit and Mars.
           6. Low  cost.  Since one  spaceship can make several or even
              many  trips, the average mission cost will drop with each
              mission.  The primary fuel, i.e. the projectiles, will be
              manufactured  on the Moon  and  therefore  should be rel-
              atively low cost. Once the lunar polar EMPL and spaceship
              are  built, the  system will  be paid  for and subsequent
              missions to Mars will cost almost nothing.


                 No  fancy equations or physics are required to explain
           this  invention.  Simple concepts will do. Table 4 shows the
           acceleration  required  in thousands of Earth gravities (KG)
           to  achieve  the given velocity, V, in kilometers per second
           for  electromagnetic projectile launchers of various lengths
           from 2 kilometers to 10 kilometers. The columns labeled by T
           give  the  time  in  seconds  necessary to achieve the given
           velocity. Recall from basic physics that velocity equals the
           product  of  acceleration  times time for a constant rate of
           acceleration.  Also  for  a  constant  rate of acceleration,
           distance  traveled  equals  one half of the product of that
           acceleration  times  the  square  of  the time. Expressed in
           equations we have:

                V = A * T                                           (1)
                D = 0.5 * A * T * T                                 (2)

           By  squaring  the  first  equation and substituting into the
           second equation we get:

                D = V * V / ( 2 * A )          or                   (3)
                A = V * V / ( 2 * D )                               (4)

           Equation  (4)  was  used to calculate the results of table 4
           which  were  converted to KGs by dividing the result by 9800
           meters  per  second  per  second.  By  substituting for A in
           equation (1) from equation (4) we get:

                T = 2 * D / V                                       (5)

                                 Table 4
                          LENGTH OF EMPL IN KILOMETERS
                     4            6            8           10
            V     KG   T       KG   T       KG   T       KG   T
            5    0.32 1.60    0.21 2.40    0.16 3.20    0.13 4.00
           10    1.28 0.80    0.85 1.20    0.64 1.60    0.51 2.00
           15    2.87 0.53    1.91 0.80    1.43 1.07    1.15 1.33
           20    5.10 0.40    3.40 0.60    2.55 0.80    2.04 1.00
           25    7.97 0.32    5.31 0.48    3.99 0.64    3.19 0.80
           30   11.48 0.27    7.65 0.40    5.74 0.53    4.59 0.67
           35   15.62 0.23   10.42 0.34    7.81 0.46    6.25 0.57
           40   20.41 0.20   13.61 0.30   10.20 0.40    8.16 0.50
           45   25.83 0.18   17.22 0.27   12.91 0.36   10.33 0.44
           50   31.89 0.16   21.26 0.24   15.94 0.32   12.76 0.40

                 It  is  important  to  know  how  many  of these smart
           projectiles  are  required  to propel the spaceship. Table 5
           shows the number of projectiles required (N) to increase the
           velocity of the spaceship by approximately one kilometer per
           second.  The  column  labeled  V  is  the  velocity  of the
           projectiles  as they leave the first electromagnetic projec-
           tile  launcher  in kilometers per second. Of critical impor-
           tance  here is the ratio of the mass of the spaceship to the
           mass  of  the  projectiles.  Let that ratio be denoted by R,
           then we have:

                 R = mass of spaceship / mass of projectile         (6)

           Let us define the following variables:
                 m  =  mass of projectile
                 v  =  velocity of projectile
                 p  =  momentum of projectile
                 M  =  mass of spaceship
                 V  =  velocity of spaceship
                 P  =  momentum of spaceship
                 M' =  new mass of spaceship
                 V' =  new velocity of spaceship

           The  momentum  of  the  projectile  as  it  approaches   the
           spaceship  will  be  given  by  the  product of its relative
           velocity and its mass:

                 p  =  ( v - V ) * m                                (7)

           The  momentum  of  the projectile will be transferred to the
           spaceship  (  plus the projectile ) when the electromagnetic
           projectile  launcher  on  board  the  spaceship  catches the
           projectile.  We  can  calculate  the velocity change for the
           spaceship from the law of conservation of momentum.

                dV  =  p / M'                                or     (8)
                dV  =  ( v - V ) * m / ( M + m )             or     (9)
                dV  =  ( v - V ) / ( R + 1 )                       (10)

           Notice  that  the  mass  of  the  projectile cancels out in
           equation  (10)  leaving  us  with the ratio. Now we have the

                M'  =  M + m  =  m * ( R + 1 )                     (11)
                dV  =  ( v - V ) * m / M'                          (12)
                V'  =  V + dV                                      (13)

           By  iteratively  recalculating equations (11),(12), and (13)
           we can find a number N such that the final mass and velocity
           of the spaceship are given by:

                M'  =   M + N * m                                  (14)
                V'  >=  V + 500                                    (15)

           The spaceship has now caught N  projectiles and next we will
           throw them back. In a similar  manner we find the following:

                dV  =  v * m / M                                   (16)
                M'  =  M - m                                       (17)
                V'  =  V + dV                                      (18)

           Notice that in equation (16) there is  no subtraction of the
           velocity  of  the spaceship. This is because the velocity of
           the  spaceship  relative  to  itself  is zero. After we have
           thrown  all  the  projectiles,  we find that the mass of the
           spaceship  is back to its original value and the velocity of
           the  spaceship  is  at least one kilometer per second faster
           than  when  we  started.  The  columns labeled VEL give the
           actual  calculated  velocity  increase  of  the spaceship in
           meters  per  second.  These  numbers  are  shown for various
           values of R, the mass ratio.

                                   Table 5
                             MASS RATIO IN THOUSANDS
                    1            2            3            4
            V    N  VEL       N  VEL       N  VEL       N  VEL
            5  112 1004.25  223 1000.09  334 1000.37  445 1000.50
           10   53 1009.51  106 1004.64  158 1000.17  211 1000.07
           15   35 1008.02   69 1001.39  104 1003.68  138 1001.45
           20   26 1019.92   52 1000.06   77 1000.59  103 1000.49
           25   21 1008.53   41 1009.39   62 1000.86   82 1003.21
           30   17 1006.93   34 1007.06   51 1007.10   68 1007.12
           35   15 1003.11   29 1003.97   44 1003.77   58 1004.04
           40   13 1029.71   26 1009.85   38 1003.73   51 1000.29
           45   12 1025.16   23 1003.54   34 1011.33   45 1003.97
           50   11 1040.79   21 1016.69   31 1008.65   41 1004.63

                 Now  we  wish  to  calculate  the  acceleration of the
           spaceship  during  the  catching and throwing of the projec-
           tiles.  This  is  important  because  humans are fragile and
           cannot  tolerate  very  high  accelerations. For this calcu-
           lation  we  have selected a electromagnetic projectile laun-
           cher  6  kilometers  in  length.  We assume it is capable of
           launching  projectiles  according  to table 4. Therefore the
           time  to  catch (or launch) a projectile will be the same as
           in  table  4.  Again  V is in kilometers per second and T in
           seconds.  It  is  clear that the more massive the spaceship,
           the  less  will  be  its  acceleration. The deceleration (or
           acceleration)  of  the  projectile is given by equation (4).
           The acceleration of the spaceship will be approximately:

                a = dV / dt                 or                     (19)
                a = V * m / M / dt          from (16)   or         (20)
                a = V / R / dt              or                     (21)
                a = V / ( R * dt )          but dt = T from (5)    (22)
                a = V / ( R * 2 * D / V )   or                     (23)
                a = V * V / ( 2 * D * R )   substituting from (4)  (24)
                a = A / R                                          (25)

           Notice  that the acceleration experienced by the spaceship is
           quite  acceptable  for  velocities  up  to 25 kilometers per
           second  when  the  mass  ratio is two or three thousand. The
           columns labeled G are in Earth gravities.

                                 Table 6
                           MASS RATIO IN THOUSANDS
                     1            2            3            4
            V      G   T        G   T        G   T        G   T
            5    0.21 2.40    0.11 2.40    0.07 2.40    0.05 2.40
           10    0.85 1.20    0.42 1.20    0.28 1.20    0.21 1.20
           15    1.91 0.80    0.96 0.80    0.64 0.80    0.48 0.80
           20    3.40 0.60    1.70 0.60    1.13 0.60    0.85 0.60
           25    5.31 0.48    2.66 0.48    1.77 0.48    1.33 0.48
           30    7.65 0.40    3.82 0.40    2.55 0.40    1.91 0.40
           35   10.41 0.34    5.21 0.34    3.47 0.34    2.60 0.34
           40   13.59 0.30    6.80 0.30    4.53 0.30    3.40 0.30
           45   17.20 0.27    8.61 0.27    5.74 0.27    4.30 0.27
           50   21.24 0.24   10.62 0.24    7.08 0.24    5.31 0.24

              This table (7) gives the same data as table 6 except that
           the  length  of  the  on  board  electromagnetic  projectile
           launcher  is  10  kilometers  instead  of 6 kilometers as in
           table 6.

                                 Table 7
                           MASS RATIO IN THOUSANDS
                     1            2            3            4
            V      G   T        G   T        G   T        G   T
            5    0.13 4.00    0.06 4.00    0.04 4.00    0.03 4.00
           10    0.51 2.00    0.25 2.00    0.17 2.00    0.13 2.00
           15    1.15 1.33    0.57 1.33    0.38 1.33    0.29 1.33
           20    2.04 1.00    1.02 1.00    0.68 1.00    0.51 1.00
           25    3.19 0.80    1.59 0.80    1.06 0.80    0.80 0.80
           30    4.59 0.67    2.29 0.67    1.53 0.67    1.15 0.67
           35    6.24 0.57    3.12 0.57    2.08 0.57    1.56 0.57
           40    8.16 0.50    4.08 0.50    2.72 0.50    2.04 0.50
           45   10.32 0.44    5.16 0.44    3.44 0.44    2.58 0.44
           50   12.74 0.40    6.37 0.40    4.25 0.40    3.19 0.40

                 The  next  item  of  interest  is  the amount of power
           necessary to operate these electromagnetic projectile launc-
           hers  - especially the ones on board spaceships. The kinetic
           energy  of any mass is given by one half the product of that
           mass times the square of its velocity.

                E = 0.5 * m * V * V                                (26)

           If  the  launchers  could  operate  at 100% efficiency, this
           would  give  us  a  good idea of the power required. Table 8
           shows  the energy of a one kilogram projectile travelling at
           the  specified  velocity  ,V,  in kilometers per second. The
           energy,  E, from equation (26) is in mega-joules. The power,
           P,  is  given  in  mega-watts for three different lengths of
           electromagnetic  projectile  launchers.  P  is calculated by
           dividing  the  required  energy, E, by the time, T, from the
           corresponding entry of table 4.

                P = E / T             or substituting from (5)     (27)
                P = 0.5 * E * V / D                                (28)

                                Table 8
                              LENGTH OF EMPL IN KILOMETERS
                                  6         8         10
              V       E           P         P         P
              5      12.5        5.21      3.91      3.13
             10      50.0       41.67     31.25     25.00
             15     112.5      127.84    105.14     84.59
             20     200.0      333.33    250.00    200.00
             25     312.5      651.04    488.28    390.63
             30     450.0     1125.      849.      671.
             35     612.5     1801.     1331.     1074.
             40     800.0     2666.     2000.     1600.
             45    1012.5     3750.     2812.     2301.
             50    1250.0     5208.     3906.     3125.

                In order to propel a spaceship of the expected size and
           mass,  it  will  be  necessary  to  use  much  more  massive
           projectiles  than  1  kilogram.  Projectiles  of  about 1000
           kilograms  will  be required. Fortunately this does not mean
           that  we  will  need  1000 times the power. The power requi-
           rements of table 8 were for continuous operation but such is
           not  required.  Electromagnetic  projectile launchers can be
           operated  or powered by capacitors which we may take as long
           as  we wish to charge up. This is clearly a tradeoff wherein
           we  can  manage  with less power if we are willing to accept
           the  penalty  of  lengthy capacitor charging periods between
           each  projectile launch. To achieve 1000 times the energy of
           table  8,  we  can  use  10 times the power applied over 100
           times  the  time.  In  other  words,  we will take about 100
           seconds to charge up the capacitors of the EMPL fully, using
           10  times  the power given in table 8 in order to launch (or
           catch)  each  projectile. Table 9 shows the time, T(in days)
           required  to  accelerate  the spaceship by one kilometer per
           second. The number of projectiles, N, was calculated exactly
           as  in  table 5. The velocity of the projectiles relative to
           the  spaceship  is V, in kilometers per second. The power of
           the  on board EMPL (in megawatts) is indicated by the column
           headers  in the table. The mass ratio, R, used was 3000, the
           mass  of  the projectiles was 1000 kilograms, and the length
           of  the  ship's  EMPL  was  assumed  to be 6 kilometers. The
           energy  of each projectile was calculated from equation (26)
           -  with  'm'  set  to 1000 kilograms. The capacitor charging
           time(in minutes) is then given by:

                CT = E/P/60.0;                                     (29)

           Where  P  is the power of the spaceship's EMPL in megawatts.
           We  have  allowed  10%  extra  time  between each projectile
           launch.  Therefore,  the  time  between  projectiles, DT (in
           minutes), is given by:

                DT = 1.1 * CT;                                     (30)

           The total time, T (in days), is therefore given by:

                T = 2 * DT * N / 60.0 / 24.0;                      (31)

                                     Table 9
                              POWER OF SPACESHIP'S EMPL IN MW
                       200                500                1000
            V     N     DT    T       N    DT    T       N    DT    T
            5    334   1.04  0.53    334  0.42  0.21    334  0.21  0.11
            6    273   1.50  0.63    273  0.60  0.25    273  0.30  0.13
            7    231   2.04  0.72    231  0.82  0.29    231  0.41  0.14
            8    200   2.67  0.81    200  1.07  0.33    200  0.53  0.16
            9    177   3.38  0.91    177  1.35  0.37    177  0.68  0.18
           10    158   4.17  1.01    158  1.67  0.40    158  0.83  0.20
           11    143   5.04  1.10    143  2.02  0.44    143  1.01  0.22
           12    131   6.00  1.20    131  2.40  0.48    131  1.20  0.24
           13    120   7.04  1.29    120  2.82  0.52    120  1.41  0.26
           14    112   8.17  1.40    112  3.27  0.56    112  1.63  0.28
           15    104   9.38  1.49    104  3.75  0.60    104  1.88  0.30


                The weight to power  ratio  given  above  was 0.2 MT/MW
           which is much better than the SP-100  specification which is
           about 30 MT/MW.  However, Brookhaven National Laboratory has
           built a gas core particle-bed reactor that can produce 200MW
           from a 300kg 1.0x0.56 meter package [1, p.302]. That amounts
           to a weight to power ratio of 0.0015 MT/MW.  The plasma from
           the reactor could be run through a magnetohydrodynamic (MHD)
           generator to convert the power into electricity  while still
           keeping the mass low.  Current  experiments indicate  that a
           power density of 40MW per liter is possible [4,p.20-1]. That
           scales up to 40,000MW per cubic meter, which is what we need
           to get to Saturn.  Superconducting  magnetic  energy storage
           (SMES) systems may be used  instead of  capacitors to  store
           the  energy to  drive the  EMPLs, but that can be determined
           at a later date.


                A way to reach the planets is now available.  Will any-
           body listen? I have written a book called "JOBS for the 21st
           Century"  which  describes my plan to visit Mars and Jupiter
           in  detail.  If you  are  interested  please  contact me at:
           C.R. Willis, 3311 Santa Monica Dr., Denton, TX., 76205 or at


           1. "Guide to the Strategic Defense Initiative", ed. by R. H.
              Buenneke & J.A. Vedda, ISBN 0-935453-11-3.
           2. "The High Frontier", G.K. O'Neill,  ISBN 0-688-03133-1.
           3. "Interstellar Propulsion Using a Pellet Stream for Momen-
              tum Transfer", C.E. Singer, JBIS v33, 1980, p.107-116.
           4. "Aviation Week and Space Technology", 1/20/92.