I get different result than stated in the book.(adsbygoogle = window.adsbygoogle || []).push({});

What am I doing wrong?

1. The problem statement, all variables and given/known data

A spacecraft returning from a lunar mission approaches earth on a hyperbolic trajectory.

At its closest approach A it is at an altitude of 5000 km, traveling at 10 km/s. At

A retrorockets are ﬁred to lower the spacecraft into a 500 km altitude circular orbit,

where it is to rendezvous with a space station.

Verify that the total delta-v required to lower the spacecraft from the hyperbola into the parking orbit is 6.415 km/s.

r_{Earth}= 6378

Gravitational parameter μ = 398600

2. Relevant equations

r - radius

e - eccentricity

A - apogee

P - perigee

h - angular momentum

v - velocity

r = altitude + r_{Earth}

e = (r_{A}- r_{P}) / (r_{A}+ r_{P})

r_{P}= (h^{2}/μ)*(1/(1+e))

v_{A}= h/r_{A}

v_{P}= h/r_{P}

v_{circular}= sqrt(μ/r)

3. The attempt at a solution

I get h = 58458,

Speed at apogee of the transfer orbit:

v_{A}= 5.1378 km/s,

Delta-v at apogee:

Δv_{A}= 10-5.1378 = 4.86219 km/s

Speed at perigee of the transfer orbit:

v_{P}= 58458/6878 = 8.499 km/s

Speed of the final orbit:

v_{circular}= 7.6127 km/h

Delta-v at perigee:

Δv_{P}= 8.499 - 7.6127 = 0.8866 km/s

Total delta-v:

Δv_{T}= 4.86219 + 0.8866 = 5.749 km/s

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# Homework Help: Delta-v for Hohmann transfer from hyperbolic trajectory to circular orbit

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