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AERO 426 HW 1, Problem 1

Team 1. AERO 426 HW 1, Problem 1. Sara h Nelson, Rebecca Hay, Michael Kim, Ricky Casurez , Jordan Bishop, Matthew Zelisko. Problem Statement and Equations.

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AERO 426 HW 1, Problem 1

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  1. Team 1 AERO 426 HW 1, Problem 1 Sarah Nelson, Rebecca Hay, Michael Kim, Ricky Casurez, Jordan Bishop, Matthew Zelisko

  2. Problem Statement and Equations • Consider transferring from the initial 300 km circular earth orbit to the starting position on the solar orbit using the escape hyperbola shown below in Figure 2. There is one impulsive burn directed along the velocity vector of the Earth orbit. Determine the required ΔV as a function of the asymptotic escape speed, Vinf. • Equations • Conservation of energy: 1/2 v2+μ/r = E • Energy of a circular orbit: Ecircular = - μ/2r • Δv = v1 – v0

  3. Solution Method • Solve conservation of energy for the initial circular orbit for the velocity • ½ v02 – μ/r = -2μ/r • V0 = (μ/r)0.5 • Solve conservation of energy for the hyperbolic transfer orbit for the velocity • ½ v12 – μ/r = E • Due to r  ∞ for the hyperbola, E is approximately v∞2/2 • ½ v12 – μ/r = v∞2/2 • V1 = (v∞2 + 2μ/r )0.5 • Calculate the difference in the velocities • Δv = v1 – v0 = (v∞2 + 2μ/r )0.5 - (μ/r)0.5

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