## Protection of the Earth from Asteroids By Alexander Bolonkin New York 2012
- Navigate this page:
- Collision avoidance strategies
- Nuclear weapons
- Kinetic impact by spacecraft
The Hiroshima nuclear bomb had power about 15 kilotons of TNT explosive. The small ball asteroid having diameter 10 m has energy in 4 times more for speed 16 km/s. 1. Equations for computation of trajectory in vacuum space near Earth.
These equations are following:
_{ (1)}
_{where }_{r}_{ is radius from Earth center to point in trajectory, m; }_{p}_{ is ellipse parament, m; }_{e }_{is ellipse eccentricity, }_{e }_{= 0 for circle trajectory, }_{e}_{ < 1 for ellipse, }_{e}_{ = 1 for parabola, }_{e}_{ > 1 for hyperbola; }_{β }_{is angle from perigee, }_{K }_{is Earth constant, }_{v}_{ is speed, m/s; }_{ν}_{ is angle between speed and tangent to circle; }_{M}_{ = 5.976}^{.}_{10}^{24 }_{kg is mass of Earth; }_{R}_{ = 6378 km is Earth radius; }_{r}_{a}_{ is apogee, m; }_{r}_{p}_{ is perigee, m; }_{b}_{ is small semi axis of ellipse, m; }_{a}_{ is small semi axis of ellipse, m; }_{T}_{ is period of rotation, sec. }
2. Change asteroid trajectory by impact of space apparatus.
Inelastic head-on collision space apparatus (SA) in the asteroid (As): (2) Where Let us place the origin at the center of gravity of an asteroid. The speed of system asteroid-SA will be
Where Δ . Let us take the asteroid having diameter 10 m ( = 1830 tons) and SA having mass = 10 tons and speed about asteroid ExampleV = 1 km/s. From equation (3)-(2) we find ΔV = 5.43 m/s, η = 0.00543.
3. Change trajectory by conventional plate explosive located on the asteroid surface.
In this case we get the impulse from the explosive gas. The maximal speed of an explosion gas and asteroid speed received from explosion are (4) where is speed of explosion gas, m/s; q is specific energy of the explosive, J/kg (q ≈ 5.4 MJ/kg for TNT), is asteroid speed received from explosion, m/s; is mass of explosive, kg; is mass of asteroid, kg.
. Let us take the asteroid having diameter 10 m ( = 1830 tons) and explosive having mass = 10 tons and specific energy of the explosive Exampleq ≈ 4.2 MJ/kg. From equation (4) we find the change of speed of asteroids = ΔV = 15.8 m/s.
If explosive is not plate (not optimum) and located in one point (ball) on the asteroid surface, the effect from the explosion will be less. Maximum speed is π/4 = 0.785 from the plate explosion speed:
= Δ V = 15.8×0.785 = 12.4 m/s.
3. Nuclear point explosion on the asteroid surface. In this case the asteroid gets the impulse from evaporation part of asteroid. The asteroid rest can get the significant speed. If the energy of the nuclear bomb is (5) where is speed of evaporation gas, m/s; λ is specific energy of the asteroid evaporation, J/kg (heating + melting + heating + evaporation), v is the volume of a sold evaporation mass, m³; ρ is the asteroid density kg/ m³; I is impulse, kg m/s; is change of the asteroid speed received from nuclear explosion, m/s; is the asteroid evaporation mass in explosion, kg; is initial mass of asteroid, kg; r is radius of explosion cavity, m.
For basalt the λ ≈ 8200 kJ/kg, E = 1 kton = 4.2 · J. From equation (4) we find = 2863 m/s; =256 tons, the change of speed of asteroids = ΔV = 460 m/s.
The impact from nuclear explosion is very strong and aster0id may spell.
Conclusion
For protection of the Earth from asteroids we need in methods for changing the asteroid trajectory and theory for an estimation or computation the impulse which produces these methods. Author develops some methods of this computation. There are: impact of the space apparatus to asteroid, explosion the conventional explosive on asteroid surface having form of plate and ball, explosion the small nuclear bomb on the asteroids surface.
The reader finds useful information about protection methods also in [1]-[8]. References
1. Asteroid Retrieval Feasibility,(2012) ESA ESTEC: March 14, 2012, Louis Friedman & Marco Tantardini http://www.kiss.caltech.edu/study/asteroid/20120314_ESA_ESTEC.pdf
2. Bolonkin A.A., (2005). Asteroids as propulsion system of space ship,
, Vol. 56, No.3/4, 2003 pp. 98-107. And Chapter 11 in book BolonkinA.A.,
Interplanetary Society Non-Rocket Space Launch and Flight, Elsevier, 2005, 488 pgs.
http://www.archive.org/details/Non-rocketSpaceLaunchAndFlight ,
http://www.scribd.com/doc/24056182
3. Bolonkin A.A., (2006). A New Method of Atmospheric Reentry for Space Ships. Presented asBolonkin’s paper
AIAA- 2006-6985 in Multidisciplinary Analyses and Optimization Conference, 6-8 September 2006, Fortsmouth.
Virginia, USA. Or Chapter 8, in Bolonkin A.A., “ New Concepts, Ideas, Innovations in Aerospace,
Technology and the Human Sciences”, NOVA, 2006, 510 pgs. http://www.scribd.com/doc/24057071 ,
http://www.archive.org/details/NewConceptsIfeasAndInnovationsInAerospaceTechnologyAndHumanSciences
4. Bolonkin A.A., (2006). “Non Rocket Space Launch and Flight”. Elsevier, 2005. 488 pgs. http://www.archive.org/details/Non-rocketSpaceLaunchAndFlight ,
http://www.scribd.com/doc/24056182 .
5. Bolonkin A.A., (2006). “New Concepts, Ideas, Innovations in Aerospace, Technology and the Human Sciences”, NOVA, 2006, 510 pgs. ISBN-13: 978-1-60021-787-6. http://www.scribd.com/doc/24057071 ,
http://www.archive.org/details/NewConceptsIfeasAndInnovationsInAerospaceTechnologyAndHumanSciences
6. Bolonkin A.A., Cathcart R.B. (2006). “Macro-Projects: Environments and Technologies”, NOVA, 2007, 536 pgs. http://www.scribd.com/doc/24057930 .
http://www.archive.org/details/Macro-projectsEnvironmentsAndTechnologies
7. Bolonkin A.A., (2006). Femtotechnologies and Revolutionary Projects. Scribd, USA, 2011. 538 p. 16 Mb. http://www.scribd.com/doc/75519828/
http://www.archive.org/details/FemtotechnologiesAndRevolutionaryProjects
8. Wikipedia. Asteroids. September 2012 Download 83.8 Kb. Share with your friends: |