Space Physics Formulas: Complement to Physics · PDF fileSpace Physics Formulas: Complement to...
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Space Physics Formulas: Complement to Physics Handbook Charge density and current density from particle species s: ρ = X s q s n s , j = X s q s n s v s Galilean transformations: E 0 = E + v × B, B 0 = B Dipole magnetic field: B(r, θ)= -B 0 R 0 r 3 2 ˆ r cos θ + ˆ θ sin θ Dipole field lines: r/ sin 2 θ = const. Magnetic field energy density and pressure: w B = p B = B 2 2μ 0 Equation of motion of neutral gas: ρ m dv dt = -∇p + other forces Equation of motion of gas of charged particle species s: m s n s dv s dt = n s q s (E + v s × B) -∇p s +o.f . MHD equation of motion: ρ m dv dt = j × B -∇p +o.f . = -∇ p + B 2 2μ 0 + 1 μ 0 (B·∇) B +o.f . Equation of continuity: ∂n ∂t + ∇· (nv)= Q - L Equation of state for ideal gas: p = nKT Dynamic pressure: p dyn = 1 2 nmv 2 Condition for ”frozen-in” magnetic field: E + v × B =0 Ohm’s law: j = σ P -σ H 0 σ H σ P 0 0 0 σ k E x E y E k = σ P E ⊥ + σ H B × E ⊥ B + σ k E k Conductivities: σ P = ne B ωci νi ω 2 ci +ν 2 i + ωceνe ω 2 ce +ν 2 e σ H = ne B ω 2 ci ω 2 ci +ν 2 i - ω 2 ce ω 2 ce +ν 2 e σ k = ne 2 1 mi νi + 1 meνe 1
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Transcript of Space Physics Formulas: Complement to Physics · PDF fileSpace Physics Formulas: Complement to...
Space Physics Formulas:Complement to Physics HandbookCharge density and current density from particle species s:
ρ =∑s
qsns, j =∑s
qsnsvs
Galilean transformations:E′ = E + v ×B, B′ = B
Dipole magnetic field:
B(r, θ) = −B0
(R0
r
)3 (2r̂ cos θ + θ̂ sin θ
)Dipole field lines:
r/ sin2 θ = const.
Magnetic field energy density and pressure:
wB = pB =B2
2µ0
Equation of motion of neutral gas:
ρmdv
dt= −∇p+ other forces
Equation of motion of gas of charged particle species s:
msnsdvs
dt= nsqs(E + vs ×B)−∇ps + o.f.
MHD equation of motion:
ρmdv
dt= j×B−∇p+ o.f. = −∇
(p+
B2
2µ0
)+
1
µ0(B·∇)B + o.f.
Equation of continuity:∂n
∂t+∇ · (nv) = Q− L
Equation of state for ideal gas:p = nKT
Dynamic pressure:
pdyn =1
2nmv2
Condition for ”frozen-in” magnetic field:E + v ×B = 0
Ohm’s law:
j =
σP −σH 0σH σP 00 0 σ‖
ExEyE‖
= σPE⊥ + σHB×E⊥
B+ σ‖E‖
Conductivities:σP = ne
B
(ωciνiω2
ci+ν2
i
+ ωceνeω2
ce+ν2e
)σH = ne
B
(ω2
ci
ω2ci+ν2
i
− ω2ce
ω2ce+ν
2e
)σ‖ = ne2
(1
miνi+ 1
meνe
)1
Cyclotron frequency (gyrofrequency):
fc = ωc/(2π) =1
2π
qB
m
Magnetic moment of charged particle gyrating in magnetic field:
µ =1
2mv2⊥/B
Magnetic force on magnetic dipole:FB = −µ∇B
Drift motion due to general force F:
vF =F×B
qB2
Pitch angle:tanα = v⊥/v‖
Electrostatic potential from charge Q in a plasma:
Φ(r) =Q
4πε0
e−r/λD
r
Debye length:
λD =
√ε0KT
ne2
Plasma frequency:
fp = ωp/(2π) =1
2π
√ne2
ε0me
Rocket thrust:T = ve
dm
dt
Specific impulse:
Isp =
∫T dt
mfuelg= ve/g
The rocket equation:
∆v = −gtburn + ve ln
(1 +
mfuel
mpayload+structure
)Total energy of elliptic orbit of semimajor axis a:
E = −GMm
2a
Emitted thermal radiation power:Pe = εσAeT
4
Absorbed solar radiation power:Pa = αAaIrad
aie171019
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