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Specific Orbital Angular Momentum
Angular momentum per unit mass of an orbiting body, conserved throughout an unperturbed orbit.
Interpretation
Specific orbital angular momentum: h = r·v·cos(γ), where γ is flight path angle. It is the angular momentum per unit mass. Example: For circular orbit, γ=0, h = r·v.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| h | Specific angular momentum | m2/s |
| r | Radial distance | m |
| v | Orbital speed | m/s |
| γ | Flight path angle | deg |
What it means
Specific angular momentum is a conserved quantity in central force motion, equal to the cross product of position and velocity. It defines the orbital plane and the shape of the orbit (semi‑latus rectum p = h²/μ). It is used in orbit determination and in the calculation of orbital elements. Understanding h is essential for orbital mechanics and for analysing perturbed orbits.
Worked example
Specific Orbital Angular Momentum – Two Examples
Real‑World| Parameter | Value |
|---|---|
| r | 6.678×10⁶ |
| v | 7726 |
| γ | 0° |
| Parameter | Value |
|---|---|
| r | 4.216×10⁷ |
| v | 3075 |
Common mistakes
- Specific orbital angular momentum: h = r·v·cos(γ).
- γ: Flight path angle (angle between velocity and local horizontal).
- For circular orbit, γ=0, so h = r·v.
- Units: m²/s.
- Constant for a given orbit.
Applications
Specific orbital angular momentum, h = r·v·cosγ, is the angular momentum per unit mass, a conserved quantity in central force motion. It determines the shape and orientation of the orbit. Engineers use h to compute the semi‑latus rectum and eccentricity, and to design orbital manoeuvres. It is essential for determining the orbit's geometry and for targeting. By understanding angular momentum, aerospace engineers can predict the path of spacecraft and plan orbit changes with precision.
- Orbit determination and parameter estimation
- Trajectory design and targeting
- Computation of orbital elements from position and velocity
- Orbital rendezvous and interplanetary navigation
- Analysis of perturbations and orbital decay
Frequently Asked Questions
It is the angular momentum per unit mass of an orbiting body, conserved throughout an unperturbed orbit. It is used to determine the orbital orientation and eccentricity.
h = specific angular momentum (m²/s)
r = orbital radius (m)
v = orbital speed (m/s)
γ = flight path angle (angle between velocity and local horizontal)
It is a constant of the motion for the two‑body problem. It determines the orbital plane and the shape (via the semi‑latus rectum).
- Assuming flight path angle γ = 0 always; it is only zero at perigee/apogee of an elliptical orbit, not generally.
- Using the wrong units for r and v.
- Confusing specific angular momentum with total angular momentum.
At perigee, r = 7,000 km, v = 8,000 m/s, and γ = 0. h = 7,000,000 × 8000 = 5.6×10¹⁰ m²/s.
The semi‑latus rectum p = h²/μ. The orbit equation is r = p/(1 + e·cos(θ)).
A tangential burn changes the speed without changing the direction, thus changing h.
At a given radius, the transverse component vθ = h/r, and the radial component vr = √(v² − vθ²).
For a circular orbit, h = r·v = √(μ·r).
It is a vector; the magnitude is invariant, but the vector direction changes with inclination.