THE DISCOVERY OF GEOMAGNETICALLY
TRAPPED COSMIC-RAY ANTIPROTONS
Astro. J. Letters 737:L29, 2011 August 20
DOI: 10.1088/2041-8205/737/2/l29
http://iopscience.iop.org/2041-8205/737/2/L29/
The key sentence from that abstract is
"PAMELA data show that the magnetospheric antiproton flux in the SAA exceeds the cosmic-ray antiproton flux by three orders of magnitude at the present solar minimum, and exceeds the sub-cutoff antiproton flux outside radiation belts by four orders of magnitude, constituting the most abundant source of antiprotons near the Earth."
The cosmic ray flux is estimated in another paper on the PAMELA results:
"PAMELA Results on the Cosmic-Ray
Antiproton Flux from 60 MeV to 180
GeV in Kinetic Energy"
Physical Review Letters 105, 121101 (2010)
DOI: 10.1103/PhysRevLett.105.121101
http://prl.aps.org/abstract/PRL/v105/i12/e121101
After eyeballing Fig. 1, I'd say they measured most antiprotons to be between 1 GeV and 10 GeV, with a flux of ~2x10^-2 / (GeV m^2 s sr). (sr=steradians.) The flux peaks around 2 GeV.
Rough multiplication gives an estimate of total flux:
[2x10^-2 / (GeV m^2 s sr)]*[9 GeV]*[10^14 m^2]*[4 pi sr]
= 2*10^14 antiprotons/second.
If we ignore the kinetic energy of the antiprotons, and assume there are plenty of available protons to annihilate with them, we get about 2 GeV per antiproton. This yields
The space shuttle orbiter weighs 69,000 kg empty. The escapte velocity from earth (which doesn't change much between the surface and the edge of the atmosphere) is 11.2 km/s, so the minimum energy needed to get it out of the earth's atmosphere is
[1/2]*[69,000 kg]*[11.2 km/s]^2
= 4x10^12 J
OK, so it would take about 10^8 s, or 3 years, to collect enough energy from antiproton cosmic-ray rest mass to lauch a space-shuttle size object out of Earth's gravity. And you'd have to scoop up from the entire surface area above the earth.
Now, the magnetospheric antiproton flux in the South Atlantic Anomaly
is said to be 3 orders of magnitude larger than the normal antiproton cosmic ray flux. By looking at the wikipedia page, it looks like the SAA covers about 10% of the surface area above the earth. If we were able to scoop up all of the antiprotons in the magnetospheric belt, it would then take about 10^6 s, or 11 days, to get enough energy to launch a space-shuttle sized object.
I am highly, highly unsure about these number and the assumptions that went into them, but it at least suggests it's possible to do. Lemme know if I did something stupid.
Thanks for all the work, even if you did make a math error, I appreciate your look over of the raw time to launch required for what you're talking about.
"PAMELA data show that the magnetospheric antiproton flux in the SAA exceeds the cosmic-ray antiproton flux by three orders of magnitude at the present solar minimum, and exceeds the sub-cutoff antiproton flux outside radiation belts by four orders of magnitude, constituting the most abundant source of antiprotons near the Earth."
The cosmic ray flux is estimated in another paper on the PAMELA results:
After eyeballing Fig. 1, I'd say they measured most antiprotons to be between 1 GeV and 10 GeV, with a flux of ~2x10^-2 / (GeV m^2 s sr). (sr=steradians.) The flux peaks around 2 GeV.Rough multiplication gives an estimate of total flux:
If we ignore the kinetic energy of the antiprotons, and assume there are plenty of available protons to annihilate with them, we get about 2 GeV per antiproton. This yields The space shuttle orbiter weighs 69,000 kg empty. The escapte velocity from earth (which doesn't change much between the surface and the edge of the atmosphere) is 11.2 km/s, so the minimum energy needed to get it out of the earth's atmosphere is OK, so it would take about 10^8 s, or 3 years, to collect enough energy from antiproton cosmic-ray rest mass to lauch a space-shuttle size object out of Earth's gravity. And you'd have to scoop up from the entire surface area above the earth.Now, the magnetospheric antiproton flux in the South Atlantic Anomaly
is said to be 3 orders of magnitude larger than the normal antiproton cosmic ray flux. By looking at the wikipedia page, it looks like the SAA covers about 10% of the surface area above the earth. If we were able to scoop up all of the antiprotons in the magnetospheric belt, it would then take about 10^6 s, or 11 days, to get enough energy to launch a space-shuttle sized object.I am highly, highly unsure about these number and the assumptions that went into them, but it at least suggests it's possible to do. Lemme know if I did something stupid.