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

1. Aug 18, 2011

### lujz

I get different result than stated in the book.
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.

rEarth = 6378
Gravitational parameter μ = 398600

2. Relevant equations

e - eccentricity
A - apogee
P - perigee

h - angular momentum
v - velocity

r = altitude + rEarth
e = (rA - rP) / (rA + rP)
rP = (h2/μ)*(1/(1+e))
vA = h/rA
vP = h/rP
vcircular = sqrt(μ/r)

3. The attempt at a solution

I get h = 58458,

Speed at apogee of the transfer orbit:
vA = 5.1378 km/s,

Delta-v at apogee:
ΔvA = 10-5.1378 = 4.86219 km/s

Speed at perigee of the transfer orbit:
vP = 58458/6878 = 8.499 km/s

Speed of the final orbit:
vcircular = 7.6127 km/h

Delta-v at perigee:
ΔvP = 8.499 - 7.6127 = 0.8866 km/s

Total delta-v:
ΔvT = 4.86219 + 0.8866 = 5.749 km/s

Last edited: Aug 18, 2011
2. Aug 18, 2011

### Staff: Mentor

Hi Lujz, welcome to Physics Forums.

I don't see anything wrong in your calculations. Is there perhaps an accompanying diagram that might introduce some "quirk" of the setup that is not included in the problem statement? An orbital plane change perhaps?

3. Aug 18, 2011

### lujz

Hi gneill,

The accompanying diagram is this:
[PLAIN]http://www.shrani.si/f/1l/r7/acGDhup/2/example62.png [Broken]

The original question is: "Find the location of the space station
at retroﬁre so that rendezvous will occur at B."
It then proceeds with calculations for periods and the angle in question.
Nothing I can notice that would affect total Δv.

Last edited by a moderator: May 5, 2017
4. Aug 18, 2011

### Staff: Mentor

Okay, so I don't see anything there that would affect your solution method. I suppose that the text's proposed answer is in error.

5. Aug 18, 2011

### D H

Staff Emeritus
Last edited: Aug 18, 2011