# Celestial Mechanics

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Celestial Mechanics
Orbital Maneuvers

Earth, Moon, Mars, and Beyond

Rodolfo G. Ngilangil Jr. MBA, BSAE

Impulsive Maneuvers
Impulsive maneuvers are those in which brief firings of onboard rocket motors change the magnitude and direction of the velocity vector instantaneously. The position of the spacecraft is considered to be fixed during the maneuvers. This is true for high-thrust rockets with burn times short compared with the coasting of the spacecraft.

Orbital Maneuvers - 2

Hohmann Transfer - Definition
The Hohmann transfer is an elliptical orbit tangent to both circles at its apse line. The periapse and apoapse of the transfer ellipse are the radii of the inner and outer circles.

The Hohmann transfer is the most
Determine the most efficient transfer from orbit 1 to a circular orbit of altitude 16 000 km (orbit 3), and the required delta-v.

Orbital Maneuvers - 14

Phasing Maneuvers
A phasing maneuver is a two-impulse Hohmann transfer from and back to the same orbit. Phasing maneuvers are used to change the position of a S/C in its orbit.

Orbital Maneuvers - 15

Phasing Maneuvers - Assignment 2 :
S/C at A and B are in the same orbit 1. At the instant shown, the chaser vehicle at A executes a phasing maneuver so as to catch the target S/C back at A after just one revolution of the chaser’s phasing orbit 2. What is the required total delta-v.

Orbital Maneuvers - 16

Phasing Maneuvers - ssignment 3 A
It is desired to shift the longitude of a GEO satellite from 99.1°W to 111.1 °W in three revolutions of its phasing orbit. Calculate the delta-v requirement.

Orbital Maneuvers - 17

Non-Hohmann Transfers with A Common Apse Line - 1

Transfer between two coaxial elliptical orbits in which the transfer trajectory shar es the apse line but is not necessarily tangent to either the initial or target orbit. The problem is to determi ne if there exists such a trajectory joining points A and B.

Orbital Maneuvers - 18

Non-Hohmann Transfers with A Common Apse Line - 2

rA = rB = e3 =

2 h3

1 µ 1 + e3 cos θ A 1 µ 1 + e3 cos θ B

2 h3

rB − rA rA cos θ A − rB cos θ B cos θ A −