chapter 6 orbital mechanics

Impulsive Maneuver

An idealized maneuver where Δv is applied instantaneously, changing velocity immediately while position remains unchanged

Δv

The magnitude of velocity change required to perform an orbital maneuver. It measures maneuver cost.

Specific Orbital Energy (ε)

Energy per unit mass of an orbit:

Angular Momentum (h)

Determines orbital plane and orbit size/shape.

Hohmann Transfer

Two-impulse transfer between two coplanar circular orbits using a transfer ellipse tangent to both orbits. Minimum Δv for that case.

Transfer Orbit

The temporary elliptical orbit used to move between two orbits.

Circularization Burn

A burn that adjusts velocity so the spacecraft matches the speed of the target circular orbit.

Bi-Elliptic Transfer

Three-impulse transfer that raises apogee very high before lowering periapsis to the final orbit. Can require less Δv when r2/r1>11.94

Radius Ratio

Determines whether Hohmann or bi-elliptic is more efficient.

Phasing Maneuver

A temporary orbit change that alters orbital period to adjust arrival time, then returns to original orbit.

Orbital Period (T)

Time required to complete one orbit:

Semi-Major Axis (a)

Half the long axis of an ellipse. Determines:

• Energy

• Orbital period

Non-Hohmann Transfer (Common Apse Line)

Transfer between elliptical orbits sharing the same line of apsides.

🔹 Line of Apsides

Line connecting periapsis and apoapsis.

🔹 Apse Line Rotation

Rotation of the orientation of an elliptical orbit within the same plane.

🔹 Radial Burn

Impulse applied along radius vector (toward/away from central body). Primarily affects:

• Eccentricity

• Argument of periapsis

🔹 Tangential Burn

Impulse applied along direction of motion. Primarily affects:

• Energy

• Semi-major axis

🔹 Normal Burn

Impulse applied perpendicular to orbital plane. Changes:

• Inclination

• RAAN

🔹 Plane Change Maneuver

Rotation of the orbital plane by changing the direction of velocity vector at the line of nodes.

🔹 Line of Nodes

Intersection line of two orbital planes.

🔹 Inclination (i)

Angle between orbital plane and reference plane.

🔹 RAAN (Ω)

Right Ascension of the Ascending Node. Orientation of orbital plane in inertial space.

🔹 Argument of Periapsis (ω)

Angle from ascending node to periapsis within orbital plane.

🔹 Rendezvous (Chase Maneuver)

Maneuver designed to intercept another spacecraft at the same position at the same time.

🔹 Velocity Triangle (for Plane Change)

Geometric relationship showing Δv required to rotate velocity vector by angle δ:

What determines orbital period?

Semi-major axis only.

Does angular momentum determine orbital period?

No. Orbital period depends only on semi-major axis.

During an impulsive maneuver, what remains constant?

Position

During an impulsive maneuver, what changes instantly?

Velocity

Q: Does orbital energy remain constant during a burn?

A: No. Energy changes when velocity changes.

Q: What type of burn primarily changes semi-major axis?

A: Tangential burn.

Q: What type of burn primarily changes eccentricity?

A: Radial burn.

Q: Why is a plane change essentially a direction change?

A: Because it rotates the velocity vector without primarily changing its magnitude.

Q: What geometric condition must exist to transfer between two orbital planes?

A: The spacecraft must be at the line of nodes.

Q: What happens to energy during a retrograde burn?

A: Energy decreases.

Q: What happens to energy during a prograde burn?

A: Energy increases.

Q: What does a pure radial burn not change significantly?

A: Semi-major axis.

Q: Does a phasing maneuver permanently change the orbit?

A: No. It temporarily changes period and then restores the original orbit.

Q: What does a phasing maneuver change?

A: Orbital period temporarily.

Q: Why can bi-elliptic transfer use less Δv?

A: Because major changes occur where orbital velocity is very small.

Q: When is bi-elliptic transfer more efficient than Hohmann?

A: When the radius ratio r2/r1>11.94

Q: Why does Hohmann require only two burns?

A: Because only two velocity magnitude changes are needed to enter and exit the transfer ellipse.

Q: Why is Hohmann transfer minimum Δv between coplanar circular orbits?

A: Because the transfer ellipse is tangent to both orbits, minimizing velocity mismatch.

Q: If semi-major axis decreases, what happens to period?

A: Period decreases.

Q: If semi-major axis increases, what happens to period?

A: Period increases.

Q: What happens to periapsis if you burn retrograde at apoapsis?

A: Periapsis decreases.

Q: What happens to apogee if you burn prograde at periapsis?

A: Apogee increases.

Q: Why must a plane change occur at the line of nodes?

A: Because that is where the two orbital planes intersect.

Q: Where is a plane change cheapest?

A: At apogee, where orbital velocity is lowest.

Q: Why are plane changes expensive?

A: Because Δv is proportional to orbital velocity magnitude.

Q: What type of burn changes inclination?

A: Normal burn.