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lujz
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I get different result than stated in the book.
What am I doing wrong?
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
r - radius
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)
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
What am I doing wrong?
Homework Statement
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
Homework Equations
r - radius
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)
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
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