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International Space Station celebrates 18th birthday in true style – by setting trash on fire

Captain DaFt

"Orbital mechanics is a particularly nasty branch of math"

Oof! No kidding. Just a simple one-tangent transfer orbit formula set as an example:

Calculate the eccentricity of the transfer orbit:

et = pt(DU) / r1(DU) - 1 (for an outbound transfer)

et = 1 - pt(DU) / r2(DU) (for an inbound transfer)

Calculate the semi-major axis of the transfer orbit:

at(DU) = r1(DU) / (1 - et) (for an outbound transfer)

at(DU) = r2(DU) / (1 + et) (for an inbound transfer)

Calculate the spacecraft's initial velocity (which is the same as the orbital velocity of its initial orbit):

vorb1(DU/TU) = Sqrt[mu(DU^3/TU^2) / r1(DU)]

Calculate the velocity of the transfer orbit at insertion:

v1(DU/TU) = Sqrt[mu(DU^3/TU^2) * (2 / r1(DU) - 1 / at(DU))]

Calculate the insertion burn:

DeltaV1(DU/TU) = v1(DU/TU) - vorb1(DU/TU)

Calculate the orbital velocity of the destination orbit:

vorb2(DU/TU) = Sqrt[mu(DU^3/TU^2) / r2(DU)]

Calculate the velocity of the transfer orbit at the destination:

v2(DU/TU) = Sqrt[mu(DU^3/TU^2) * (2 / r2(DU) - 1 / at(DU))]

Calculate the arrival burn:

DeltaV2(DU/TU)^2 = v2(DU/TU)^2 + vorb2(DU/TU)^2 - 2 * vorb2(DU/TU) * Sqrt[mu(DU^3/TU^2) *pt(DU)] / r2(DU)

Calculate the total DeltaV required for the transfer:

DeltaV(DU/TU) = DeltaV1(DU/TU) + DeltaV2(DU/TU)

Calculate the true anomaly at the interception point:

Cos[nu2(radians)] = (pt(DU) / r2(DU) - 1) / et (for an outbound transfer)

Cos[nu2(radians)] = (pt(DU) / r1(DU) - 1) / et (for an inbound transfer)

Calculate the eccentric anomaly at the interception point:

E(radians) = ArcCos[(et + Cos[nu(radians)]) / (1 + et * Cos[nu(radians)])] (for an outbound transfer)

E(radians) = 2 * pi - ArcCos[(et + Cos[nu(radians)]) / (1 + et * Cos[nu(radians)])] (for an inbound transfer)

Calculate the time required for the transfer:

TOF(TU) = Sqrt[at(DU)^3 / mu(DU^3/TU^2)] * (E(radians) - et * Sin[E(radians)]) (for an outbound transfer)

TOF(TU) = Sqrt[at(DU)^3 / mu(DU^3/TU^2)] * (E(radians) - et * Sin[E(radians)] - pi) (for an inbound transfer)

And yet... Toss a frisbee and your dog takes off after it, jumps and catches it perfectly, his brain doing essentially the same formula.

And this from an animal that can barely be taught to count to three!

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