Project Longshot to Alpha Centauri - part 3

Apparent and True Orbits of Alpha Centauri. Motion is shown from the A component against the relative orbital motion of B component. The Apparent Orbit (thin ellipse) is the shape of the orbit as seen by the observer on Earth. The True Orbit is the shape of the orbit viewed perpendicular to the plane of the orbital motion.

All right, done 32 out of 72 pages of Project Longshot, a proposed mission to Alpha Centauri, the closest star system to our own. The rest should take about four days, I think. Then I'll upload the whole thing to scribd.com.



2.3 Orbits

Once the probe is assembled in orbit at the space station, it will be nudged into an indpendent but similar orbit to prevent damage to the station due to the exhaust from the first upper-stage burn (see Fig. 2.3a). This burn will be made to increase the inclination of the probe orbit from 28.5 degrees to 37.5 degrees so that it will sum with the obliquity and result in an orbit inclined 61 degrees relative to the ecliptic. This stage will be jettisoned, and the spacecraft will then escape Earth with a second burn which occurs at the ascending node of the probe's orbit about the earth (see Fig. 2.3b). This point then becomes the ascending node of the probe's heliocentric orbit, which is a circular orbit at 1 AU and at an inclination of 61 degrees. The second stage will then separate, and three months (i.e. one-fourth of an orbit) later, the third and final upper-stage will burn. This will send the spacecraft on an escape trajectory toward the Centauri system (see Fig. 2.3c), which is located at a declination of -61 degrees to the ecliptic. Upon completion of the interstellar phase of the mission the probe will be inserted into an eccentric orbit about Beta (see Figs. 2.3d and 2.3e).


Text:
ECLIPTIC
61.0°
52.0°
BURN #1

Text:
ECLIPTIC
61.0°
BURN #2

Text:
BURN #3
ECLIPTIC
61°
TO CENTAURI SYSTEM

Text:
SYSTEM INJECTION
11-35 A.U.
Probe
~1/6 lt. yr.
Fly-by
Proxima
To Sun

Text:
FINAL ORBIT ABOUT BETA CENTAURI
~11 A.U.
Probe
Rp, B, RA
ALPHA-BETA SEPARATION: 11-35 A.U.
RP ABOUT BETA: 1 A.U.
RA ABOUT BETA: 2.5 A.U.
SEMI-MAJOR AXIS: 1.75 A.U.
ECCENTRICITY: 0.429
PERIOD: 2.5 EARTH YEARS
VELOCITY AT APOGEE: 13.1 km/sec
VELOCITY AT PERIGEE: 32.9 km/sec

Assuming a space station orbit of 300 kilometers at an inclination of 28.5 degrees, the following values were determined for required velocity changes for the probe. The Alpha Centauri star system is at a declination of -61 degrees relative to the ecliptic of our solar system. At the optimum launch position, the obliquity (23.5 degrees from the eliptic) will sum with the inclination angle of the spacecraft's orbit (28.5 degrees from the equator). This will make the probe's orbit 52 degrees from the ecliptic. Thus, a 9 degree plane change is required to put the probe into a 61 degree orbit around the earth (relative to the ecliptic). From this orbit, another velocity change is necessary to escape the earth's gravity and inject the probe into a circular orbit around the sun at 1 AU and a 61 degree inclination. At this point, there are two options to be considered, depending on the fuel source, Earth or Jupiter. For the first option, the probe will leave from this orbit directly for Alpha Centauri, in which case it will change velocity at the perihelion of the transfer orbit between our solar system and Alpha Centauri. For the second option the spacecraft will transfer to a Jupiter-distanced heliocentric orbit, using a velocity change at the perihelion of the Earth to Jupiter transfer orbit, and inject into an orbit around Jupiter at a 61 degree inclination (to take on fuel). The probe will then escape back into a Jupiter-distanced heliocentric orbit at 61 degrees relative to the ecliptic). Finally, it will escape the solar system and head for Alpha Centauri, with a burn at perihelion of the Sol-Centauri transfer orbit.

(see appendix for actual number calculations)

1. Delta-V for plane change of 9 degrees: 1.2123 km/s
2. Delta-V to escape earth: 3.2002 km/s
3. Delta-V to escape solar system: 12.4273 km/s
4. Total Delta-V for Option #1: 16.8398 km/s

For Option #2, the first two numbers are the same.

5. Delta-V to enter Earth-Jupiter transfer: 8.8223 km/s
6. Delta-V to orbit around Jupiter: 7.4814 km/s
7. Delta-V to escape Jupiter: 6.1705 km/s
8. Delta-V to escape solar system 5.4087 km/s
9. Total Delta-V for Option #2: 32.2954 km/s

Obviously, the option of picking up fuel mined from the atmosphere of Jupiter would be impractical because of high cost and complication.

For the objective orbit within the Centauri system, Beta was chosen as the target star because it is a dK type star, about which we have very little data, while Alpha is a G2 type star like our own, which we have studied extensively. The orbit chosen is based on an assumption that Alpha and Beta (which vary in distance between 11 and 35 AU) will be at the lesser of the two distances. The orbit chosen is an elliptical orbit around Beta for which the aphelion lies on the line between Alpha and Beta. The perihelion radius was set at 1 AU. The aphelion was determined based on a requirement that the gravitational effect of Alpha would not exceed 5% of the gravitational effect of Beta. Accordingly, an aphelion of 2.5 AU was chosen. At this aphelion the gravitational force on the probe due to Alpha will be equal to 3.3% of the gravitational force due to Beta. Based on the chosen perihelion and aphelion radii, the orbital parameters were determined:

a = 1.75 AU
e = 0.428572
E = -216.95 kmE2/secE2
T = 2.4977 Earth years
Va = 13.1 km/s
Vp = 32.935 km/s

The perihelion velocity will be the velocity to which the probe must be slowed for proper insertion into this orbit.


3.0 SPACECRAFT SYSTEMS

3.1 Power

Power for the instruments, computer, communication lasers, and star trackers will be supplied by a 300 kilowatt nuclear reactor. This reactor will be compact-sized, have a low specific mass, long life, high reliability, and a variable power output. Different systems were compared, and a design published by Jones, MacPherson, and Nichols, of the Oak Ridge National Laboratory was chosen and scaled down to suit the needs of the Centauri mission.

This power system concept defines a nuclear reactor with ceramic fuel, clad with refractory metal, and cooled by liquid potassium (1365 K). Also described is a direct, closed Rankine power conversion cycle, and a large tetraxial flywheel energy storage system featuring graphite composite materials and magnetic bearings. The fuel is enriched uranium nitride pellets. The reactor and flywheel systems will be constructed as separate modules designed to fit in the shuttle cargo bay.

The reactor will boil potassium which will then be piped through a turbine that will convert the thermal energy to mechanical energy. The potassium is further cooled by flowing through the heat radiators and is then recycled back into the reactor.

The electrical current produced by the spinning turbine is directed to the two (for redundancy) energy storage systems located at either end of the main structural truss. The modules contain flywheels which story the energy in their spin rate, and also provide attitude control by absorbing external torques.

Mass

reactor - 500 kg
shielding - 830 kg
turbine - 230 kg
piping and miscellaneous - 680 kg
8 flywheels - 3400 kg
flywheel motors, structure - 760 kg
Total mass - 6400 kg

Power output is variable but will need to be a minimum of 250 kW during the in-system phase of the mission to power the communication lasers and computer.