Further to the paper titled "Terraforming Mars: Creating a Magnetic Field" we investigate the size of the magnetopause that would be created by giving Mars a dipolar magnetic field. It is found that if the magnetic field at the equator is the same as that on Earth (31,000nT) then the stand-off distance of the magnetopause would be roughly 37000km

Checklin, Chris

Farrow, James Anthony

Hue, Jeremy

Miller, Robert

English

University of Leicester Open Journals

Journal of Physics Special TopicsA2 6 Look at the size of that!J. A. Farrow, R. Miller, J. Hue and C. ChecklinDepartment of Physics and Astronomy, University of Leicester. Leicester, LE1 7RH.Nov 20, 2014.AbstractFurther to the paper titled ”Terraforming Mars: Creating a Magnetic Field” we investigate thesize of the magnetopause that would be created by giving Mars a dipolar magnetic field. It isfound that if the magnetic field at the equator is the same as that on Earth (' 31, 000nT) thenthe stand-off distance of the magnetopause would be roughly 37000km.IntroductionPreviously we discussed how a magnetic field could be created on Mars by using a loop of copper aroundthe equator and putting a current through it. [1] Now we move on to working out what size magneto-sphere this would actually create by calculating the stand-off distance between the solar wind and themagnetopause.DiscussionAs Mars is further away from the Sun than the Earth, the flux from the solar wind will be lower. Wecalculated the solar wind mass density by using the fact that,r2ρv = constant, (1)where; r is the orbital radius of the planet, ρ is the solar wind mass density, and v is the velocity of thesolar wind. Using values of 5 × 106m-3 for the solar wind mass density at Earth, the orbital radius ofthe Earth being 1AU (1.8× 108m), the orbital radius of Mars being 1.52 AU, and v being assumed to beconstant at 500kms-1, we can calculate a value for the solar wind mass density at Mars by using Eqn.(1)to derive,ρm =r2EρEr2m. (2)The subscripts m and E denote Mars and Earth respectively, and this gives a value for ρ at Mars of3.62× 10−21kgm-3.Knowing the mass density of the solar wind at Mars we can now calculate the pressure of the solarwind using,Psw = ρv2, (3)where; P is the pressure and the subscript sw denotes the solar wind.To find the size of the magnetopause we must find the point at which the pressure of the solar windis equal to the pressure of the magnetopause, known as the stand-off distance. The pressure of themagnetopause is given by,Pmp =B2mp2µ0, (4)where; B is the magnetic field strength, the subscript mp denotes the magnetopause, and µ0 is thepermeability of free space.Equating Eqn.(3) and Eqn.(4) we can determine the magnitude of the magnetic field at the magne-topause by,Bmp =√2ρv2µ0. (5)Using ρ as determined earlier we can calculate that the magnetic field strength at the magnetopauseof Mars is 47.7nT.As Bmp is 2Bdipole [3] it is then possible to find the magnetic field strength at the magnetopause interms of the magnetic field strength at the equator through,Bmp = 2(Beq(1 + 3 cos2(θ))12(Rprmp)3), (6)1Look at the size of that!, Nov 20, 2014.where; the subscript eq denotes the equator, θ is the colatitude, Rp is the radius of the planet, and rmpis the distance to the edge of the magnetopause (stand-off).At the equator θ is 90 degrees so Eqn.(6) becomes,Bmp = 2Beq(Rprmp)3. (7)Rearranging for rmp we get,r3mp = Beq2R3pBmp. (8)Having calculated Bmp earlier, using Rp as the radius of Mars (3389.5km) [4], and assuming that Marshas the same magnetic field strength at its equator as the Earth does (31, 000nT) [2] it is possible to useEqn.(8) to calculate the size of the magnetopause. We found the value of rmp to be roughly 37, 000km.ConclusionFollowing on from our previous paper we have now shown that the standoff distance of the magnetopausecreated on Mars with a magnetic field of roughly the strength of Earth’s is 37, 000km. This is about 67%of the size of Earth’s.References[1] J. Hue, J. A. Farrow, C. Checklin and R. Miller A2 4 Terraforming Mars: Creating a Magnetic Field, PST13, (2014).[2] http://en.wikipedia.org/wiki/Terraforming_of_Mars accessed 20/11/2014[3] http://en.wikipedia.org/wiki/Magnetopause#Estimating_the_standoff_distance_to_the_magnetopause accessed 20/11/2014[4] http://en.wikipedia.org/wiki/Mars accessed 20/11/2014.2

A2_6 Look at the size of that!

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A2_6 Look at the size of that!

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