ROCKET SCIENCE

9/2/17; 12/1/17
By John Hebert

CONTENTS—
Rocket science facts
Rocket performance specifications
Rocket formulas

ROCKET SCIENCE FACTS
1. I have calculated optimistic and conservative estimates on how fast spacecraft can travel at 3 points in time: 
conservative estimates: 2035AD-23 miles per second; 2200AD-200 miles per second;2265AD (Star Trek’s time)-29% of the speed of light
optimistic estimates: 2035AD-185 miles per second; 2200AD-8,000 miles per second (4.29% of the speed of light); 2265AD-99.75% of the speed of light.
2. If the Earth were 9 inches big, then the voyager spacecraft that left the solar system travels 90 feet per day and 6 miles a per year, and would now be 174 miles away from the Earth. The proposed Orion interstellar spacecraft travels a mile a day and over 350 miles per year.
3. If a space probe were launched from the Earth at at velocity of 11.5 miles per second, and if that Earth were reduced to a 1 foot size, the Moon would be about 4 inches large, it would be 2.5 feet away from the 1 foot Earth, and it would take 2 days and 9 hour to reach the Moon. the Sun would be over 9 feet large, over 970 feet away, and it would tale the space probe 93 days to reach it. Mars would be 641 feet away and the probe would reach it in just over 2 months. Pluto would be 7.25 miles away and the probe would take just over 10 years to get there. The current distance of the earlier probe that left the solar system, Voyager 2, would be 57 miles away and our probe took 40 years to get that far. The nearest star, Alpha Centauri, would be over 50,000 miles distant and it would take the probe over 69,500 years to get there. To get to the very large star Betelguese, which is visible in the night in the Orion constellation, would take 10.5 million years to get there and the star would be 1.85 miles large. With our Earth reduced to a size of 1 foot, the largest star known would be 4.5 miles large in comparison. The Andromeda galaxy would be 29 billion miles away, and finally, the edge of the universe would be almost 92 light years away.
4. If each year that the voyager spacecraft were to equal a grain of sand, then a sphere 1,000 feet in diameter filled with grains of sand (years) would be how long it would take the spacecraft to cross the universe from one end to the other end.
5. To launch the Saturn 5 rocket, the amount of antimatter need to do it would be 17.155 grams, or 1/26.5 pounds of antimatter. This would require 10 trillion trillion anti-hydrogen atoms of antimatter.
6. To propel a 170 pound person 1/2 of the speed of light, it would require 8.694 x 10^17 joules of energy, equivalent to 28,900 Saturn 5 launches, and would require 106.2 pounds of antimatter to do this.
7. The amount of antimatter to travel to Mars, distance 114 million miles, a 39 day trip, constant acceleration to the end velocity of 16.99 miles per second, and the mass of the rocket at 5,000 tons, the amount of antimatter needed for these specification is 18.964 grams of antimatter (equal to the weight of 6 pennies).
8. To send 1 pound of cargo to alpha Centauri in 43 years at a velocity of 10% of the speed of light using chemical rockets would require 5.9 x 10^2,147 tons of fuel to get there. In comparison, the mass of the entire universe is 3.2 x 10^50 tons .

9. With the recent interstellar mission proposal to alpha Centauri by the starshot project which will take 20 years to get there, if the earth were the size of a smoke particle, the space probe would travel 1.6 feet in a day, 11 feet a week, 44 feet a month, 528 feet in a year, and to complete the mission, 2 miles when it arrived at its destination.

10. I went for a ride in my car on 1/25/18 for a distance of 28 miles. I drove at 30 miles per hour and it took me 56 minutes. If that 28 miles per equal to 1 millimeter, then the nearest star would be 1.22 billion miles away, or 49,054 times the distance going around the earth. To drive to the nearest star at 30mph would take 95,064,263 years.

 

SEVERAL SPACECRAFT DESIGN SPECIFICATIONS
mag-sail-
velocity=63,821 meters/second (39.57 miles per second)Initial mass=53.9 tons
acceleration=.00143 meters/second^2
force=70 newtons
Kinetic energy=9.98 x 10^13 joules
Energy density=2.04 x 10^9 joules/kilogram
power=2.23 x 10^6 watts
Specific power=.0456 kilowatts/kilogram momentum=31.15 x 10^9 meters-kilogram impulse=3.13 x 10^9 newtons-second
distance=to jupiter (880 million miles)
Time for journey=517.19 days (1.416 months)

2. ion propulsion-
velocity=90,000 meters/second (55.8 miles per second) Exhaust velocity=55,860 meters/second
Isp=5,694 seconds
Mass ratio=2.5
Initial mass=486 kilograms
Final mass=220.91 kilograms
acceleration=.00284 meters/second^2
force=1.38 newtons
Kinetic energy=1.98 x 10^12 joules
Energy density=4.66 x 10^9 joules/kilogram
power=62,371.66 watts
Specific power=.128 kilowatts/kilogram
momentum=43.74 x 10^6 meters-kilogram
impulse=43.56 x 10^6 newtons-second
Fuel flow=.0000154 kilograms/second
distance=to jupiter (880 million miles)
Time for journey=365.25 days (12 months)

3. Orion
 velocity=100 kilometer/second
(62 miles per second)
Exhaust velocity=117.72 kilometers/second
Isp=12,000 seconds
 Mass ratio=2.34
 Initial mass=10,000 tons
 Final mass=4,273.5 tons
 acceleration=39.2 meters/second^2
force=356,363,363 newtons
 Kinetic energy=5.08 x 10^20 joules
 Energy density=5.59 x 10^13 joules/kilogram
power=1.78×10^13 watts
 Specific power=1,960 kilowatts/kilogram
momentum=909.1 x 10^9 meters-kilogram
impulse=1.176 x 10^15 newtons-second
 Fuel flow=.319 kilograms/second
 distance=to jupiter (880 million miles)
 Time for journey=330 days (11 months)
 How much antimatter is need if used=31 pounds

4. vasimr-
velocity=33,894.23 meters/second
(21 miles per second)
Velocity exhaust=2,625.99 meters/second
isp=267.69 seconds
Initial mass= 1,290.72 tons
Final mass=100 tons (hypothetical)
Mass ratio=12.9072
acceleration=.00103 meters/second^2
newtons=4,727.83 
Kinetic energy=6.74 x 10^14 joules
Energy density=5.744 x 10^9 joules/kilogram
power=200 megawatts
Specific power=.00951 kilowatts/kilogram
momentum=3.98 x 10^10 meters-kilogram
impulse=99.4 x 10^9 newtons-second
Fuel flow=.0558 kilograms/second
distance=to jupiter (880 million miles)
Time for journey= 243.4 days
How much antimatter is need if used=374.44 grams

5. TAU- (this craft was intended to go out 1,000 AUs) velocity=191,808 meters/second
(118.92 miles per second)
Initial mass=about 32 tons
acceleration=.00032 meters/second^2
force=9.32 newtons
Kinetic energy=5.35 x 10^14 joules
Energy density=1.9 x 10^10 joules/kilogram
power=36,000,000 watts
Specific power=1.238 kilowatts/kilogram momentum=5.58 x 10^9 meters-kilogram impulse=138,500,000 newtons-second
Fuel flow=.00196 kilograms/second
distance=to jupiter (880 million miles)
Time for journey=172 days (5.73 months)
How much antimatter is need if used=29.72 grams

6. nuclear-
velocity=117,720 meters/second
(72.99 miles per second)
Exhaust velocity=58,860 meters/second Isp=6,000 seconds
isp=6,000 seconds
Mass ratio=2
Initial mass=3,500 tons
Final mass=1,750 tons
acceleration=.012 meters/second^2
force=37,494.6 newtons
Kinetic energy=2.2 x 10^16 joules
Energy density=6.9 x 10^9 joules/kilogram
power- 2.2 billion watts
Specific power=16.61 kilowatts/kilogram momentum=3.7456 x 10^11 meters-kilogram impulse=3.7455 x 10^11 newtons-second
Fuel flow=.3185 kilograms/second
distance=to jupiter (880 million miles)
Time for journey=115.62 days (3.854 months)
How much antimatter is need if used=2.69 pounds

7. breakthrough starshot-
(intended to go to the nearest star)
velocity= 15-20% light speed
Initial mass=.001 kilograms
acceleration=100,000 meters/second^2
force=100 newtons
Kinetic energy=1.4 x 10^14 joules
Energy density=1.4 x 10^17 joules/kilogram
power=1.79 x 10^12 watts
Specific power=1.79 x 10^12 kilowatts/kilogram
momentum=45,000-60,000 meters-kilogram impulse=7.97 x 10^6 newtons-second
distance=to jupiter (880 million miles)
Time for journey=22.14 hours

8. fusion-
velocity=52,800,000 meters/second
(32,736 miles per second, or
17.6% of light speed)
Velocity exhaust=5,280,000 meters/second
isp=538,226.3 seconds
Initial mass=about 50,000 tons
Final mass=5,000 tons (hypothetical)
Mass ratio=10
acceleration=176 meter/second^2
force= 8×10^9 newtons
Kinetic energy=6.34 x 10^22 joules
Energy density=1.39 x 10^15 joules/kilogram
power=1.9 x 10^18 watts
specific power=41.8 million kilowatts/kilogram
momentum=2.4 x 10^15 meters-kilogram
impulse=2.67 x 10^14 newtons-second
Fuel flow=1,363.53 kilograms/second
distance=to jupiter (880 million miles)
Time for journey=9.26 hours
How much antimatter is need if used=3,874.4 tons

9. tau-
velocity=192,738.3 meters/second
(119.5 miles per second)
Initial mass=59.81 tons
acceleration=.0001233 meters/second^2
force=6.72 newtons-6.7 newtons
Kinetic energy=1.01 x 10^15 joules
Energy density=18,570,000,000 joules/kilogram
power=661,395 watts
Specific power=.0121 kilowatts/kilogram momentum=105.7 x 10^9 meters-kilogram impulse=102.94 x 10^9 newtons-second
Fuel flow=.000356 kilograms/second
distance=1,000 astronomical units
Time for journey=48.54 years
How much antimatter is need if used=(56.1 grams)

10. breakthrough starshot-
velocity=15-20% of the speed of light
Initial mass=.001 kilograms
acceleration=100,000 meters/second^2 force=100 newtons-100 newtons
Kinetic energy=1.01 x 10^12-1.8 x 10^12 joules
Energy density=1.01 x 10^15-1.8 x 10^15 joules/kilogram
power=2,852-1,901.3 watts
Specific power= 2,852-1,901.3 kilowatts/kilogram
momentum=45,000-60,000 meters-kilogram impulse=63 x 10^9-94.7 x 10^9 newtons-second 
distance=to Alpha Centauri (4.37 light years)
Time for journey=20-30 years

11. starship enterprise- (to the moon)
velocity-warp 1 (186,282 miles per second)
Initial mass=190,000 tons
acceleration=116.71×10^6 meters/second^2 force=2×10^16 newtons
Kinetic energy=7.77×10^24 joules
Energy density=4.5×10^16 joules/kilogram
power=3×10^24 watts
Specific power=1.75×10^13 kilowatts/kilogram momentum=5.18×10^16 meters-kilogram impulse=5.14×10^16 newtons-second
Fuel flow=443.91×10^6 kilograms/second
distance=to moon (238,000 miles)
Time for journey=2.57 seconds
How much antimatter is need if used=474,833 tons

12. starship enterprise- (to mars)
velocity=warp 1 (186,282 miles per second)
Initial mass=190,000 tons
acceleration=243,579 meters/second^2 force=4.21×10^13 newtons
Kinetic energy=7.77×10^24 joules
Energy density=4.5×10^16 joules/kilogram
power=6.31×10^21 watts
Specific power=3.65×10^10 kilowatts/kilogram momentum=5.18×10^16 meters-kilogram impulse=5.18×10^16 newtons-second
Fuel flow=140,292 kilograms/second
distance=to mars (estimate 114 million miles)
Time for journey=1,231.2 seconds (20.52 minutes)
How much antimatter is need if used=474,833 tons

13. VASIMR (FROM INTERNET)- (to mars)
velocity=34,020 meters/second (21 miles/second)
Velocity exhaust=30,000-120,000 meters/second
(from internet)
Isp=3,058-12,232 seconds
(from internet)
mr=3.108 (hypothetical estimate)
Initial mass=3,500 tons (estimate)
Final mass=1,126 tons
acceleration=.0061 meters/second^2
force=19,409.63 newtons
Kinetic energy=4.45 x 10^15 joules
Energy density=1.4 x 10^9 joules/kilogram
(from internet)
power=1.32 x 10^9 watts
Specific power=.415 kilowatts/kilogram momentum=108.25 x 10^9 meters-kilogram impulse=6.45 x 10^10 newtons-second
Fuel flow=.9443 kilograms/second
distance=to mars (estimate 142 million miles)
Time for journey=39 days
How much antimatter is need if used=247.22 grams

14. Conventional rocket- (to mars)
velocity=3.2-7.5 miles/second
Velocity exhaust=4,513-4,562 meters/second
Isp=460-465 seconds
mr=3.138-14.35
Initial mass=3,500 tons (estimate)
Final mass=1,115.5-243.9 tons
acceleration=.0000579-.000321 meters/second^2
force=184-1,021 newtons
Kinetic energy=4.236 x 10^13-2.24 x 10^14 joules
Energy density=13.3 x 10^6-70.7 x 10^9 joules/kilogram
power=1.9 x 10^6-23.78 x 10^9 watts
Specific power=.000597-7.47 kilowatts/kilogram momentum=16.42 x 10^9-38.66 x 10^9 meters-kilogram
impulse=4.1 x 10^9-9.66 x 10^9 newtons-second
Fuel flow=.1427-.3363 kilograms/second
distance=to mars (estimate 142 million miles)
Time for journey=8.6-3.65 months
How much antimatter is need if used=2.35-13.05 grams

15. 25,000 year trip to nearest star
velocity=157.17 miles/second
Velocity exhaust=n/a
Isp=n/a
mr=n/a
Initial mass=25 kilograms (estimate)
Final mass=n/a
acceleration=.00000008 meters/second^2
force=.000002 newtons
Kinetic energy=8 x 10^11 joules
Energy density=32 x 10^10 joules/kilogram
power=1.8 watts
Specific power=.00004073 kilowatts/kilogram momentum=6,365,385 meters-kilogram
impulse=1,577,880 newtons-second
Fuel flow=.000000000031688 kilograms/second
distance=4.3 light years
Time for journey=25,000 years
How much antimatter is need if used=44.4 milligrams

16. New horizon to Pluto
velocity=10.28 miles/second; 37,000 miles per hour
Velocity exhaust=n/a
Isp=n/a
mr=n/a
Initial mass=1,000 tons (estimate)
Final mass=n/a
acceleration=n/a
force=n/a
Kinetic energy=1.26 x 10^14 joules
Energy density=n/a
power=131,643 watts
Specific power=.000475 kilowatts/kilogram momentum=15.14 x 10^9 meters-kilogram
impulse=n/a
Fuel flow=n/a
distance=3 billion miles
Time for journey=9.25 years
How much antimatter is need if used=7 grams

17. Traveling to the nearest star at 3% of the speed of light. (hypothetical scenario)
velocity=.03c
Velocity exhaust=3,908,605.34 meters/second
Isp=398,435 seconds
mr=10
Initial mass=3,500 tons
Final mass=350 tons
acceleration=.1426 meters/second^2
force=543,745 newtons
Kinetic energy=1.29 x 10^20 joules
Energy density=4.05 x 10^13 joules/kilogram
power=4.09 x 10^12 watts
Specific power=.1,285.43 kilowatts/kilogram momentum=1.386 x 10^14 meters-kilogram
impulse=14.32 x 10^9 newtons-seconds
Fuel flow=.1008 kilograms/second
distance=2.84 x 10^14 miles (boost)
distance=<4.3 light years (coast)
Time for journey=1 years (boost)
Time for journey=140.736 years (coast)
How much antimatter is need if used=7.88 tons

Spaceflight formulas

Meaning of variables in the formulas—
v=velocity (meters/second)
vi=velocity initial (meters/second)
vf=velocity final (meters/second)
vexh=exhaust velocity (meters/second)
isp=seconds
m=mass (kilograms)
mi=initial mass (kilograms)
mf=final mass (kilograms)
mr=mass ratio
a=acceleration (meters/second^2)
f=force (newtons)
d=distance (meters)
t=time (seconds)
ke=kinetic energy (joules)
ed=energy density (joules/kilograms)
p=power (watts)
spp=specific power (kilowatts/kilograms)
mm=momentum (meters x kilograms)
i=impulse (thrust x seconds)
fr=fuel rate (kilograms/second)
mw=molecular weight
texh=temperature exhaust (kelvin)
eff=propulsive efficiency
r=radius (meters)
ecc=eccentricity
g=acceleration due to gravity
(9.91 meters/second^2)

Rocket equation—
velocity—
v=vexh x ln(mi/mf)
v=(d x 2)/t (when accelerating)
v=d/t (constant velocity)
v=sqrt(2 x a x d)
Velocity of exhaust—
vexh=v/ln*(mi/mf)
vexh=.25 x sqrt(texh/mw)
Isp—
isp=vexh/9.81
isp=f/(fr x 9.81)
isp=vf/(ln(mr) x 9.81)

Mass ratio—
mr=mi/mf
mr=e^(v/vexh)
mr=e^(vf/(isp x 9.81))
Mass final—
mf=mi/(e^(vf/vexh)
Mass initial—
mi=mf x e^(vf/vexh)
mass—
m=f/a
m=2 x ke/v^2
Force—
f=m*a
f=ke/d
f=9.81 x isp x fr
acceleration—
a=f/m
a=2 x d/t^2

Energy —
ke=1/2 x v^2 x m

ke=d x f
Energy density (rest mass energy)—
ed=ke/m
Fuel flow rate—
fr=f/vexh
fr=m/t
Distance —
d=v*t/2 (with respect to accelerating)
d=v x t (constant velocity)
d=ke/f
Time—
t=(d x 2)/v (constant acceleration)
t=d x v (constant velocity)
t=((m x vf)^2/2)-(m x mi)^2/2) x (1/f) x (2/vi+vf)
Power—
p=ke/t
p=f x d/t
Specific power —
sp=(p/1000)/m
Momentum —
M=v x m
Impulse —
i=f x t
Antimatter needed (kilograms)—
m=ke/1.8 x 10^16
Propulsive efficiency—
eff=2/(1+(vexh/vf))
eff=(vf/vexh)^2/(e^(vf/vexh)-1)
(Maximum efficiency for ratio- vf/vexh<1.6)
eff=f x g x isp/2 x p