Sequenced Burn Schedule & Approach Timeline
5 Planned BurnsDerived from circular-to-circular coplanar Hohmann phasing and relative co-elliptic approach vectors.
| Burn / Phase | Nominal MET | Δv Magnitude | Target Orbit (km) | Operational Objective |
|---|
The Mechanics of Space Station Resupply & Rendezvous
Getting cargo to the International Space Station is not simply a matter of pointing a rocket upward. It is an orbital synchronization problem governed by Earth's oblate gravity, planar geometry, and orbital phasing.
1. The In-Plane Launch Window & Azimuth
The International Space Station orbits at an inclination of 51.6° to Earth's equator. Because the Earth rotates once every 24 hours beneath the orbital plane, a fixed launch pad on Earth (such as Kennedy Space Center SLC-40 at latitude 28.57° N) intersects the orbital plane only twice per sidereal day: once during the ascending pass (northeast trajectory) and once during the descending pass (southeast trajectory).
βNE = arcsin(cos(51.6°) / cos(28.57°)) ≈ 42.8°
Launching outside of this instantaneous moment requires the booster to expend massive propellant performing yaw doglegs to correct plane angle (each 1° of plane change costs roughly 135 m/s of Δv in low Earth orbit).
2. Phasing Orbits & Kepler's Catch-Up Rate
After second stage separation, the cargo spacecraft (such as SpaceX Dragon, Cygnus, or Progress) is placed into a lower parking orbit—typically 200 to 300 km altitude.
By Kepler's Third Law (T = 2π√(a³/μ)), an object in a lower orbit travels faster
both in linear velocity and angular speed. At 210 km, the chaser takes ~88.6 minutes per revolution,
while the station at 418 km takes ~92.9 minutes.
Catch-up rate ≈ 16.4° per orbit ≈ 10.6° per hour
The flight controllers let the chaser phase until the angular separation matches the exact transfer lead angle, at which point the rendezvous burns commence.
3. Hohmann Transfers & Co-Elliptic Approach
Raising the chaser orbit from 210 km to the station's 418 km orbit is accomplished via a two-impulse Hohmann transfer.
Δv1 = √(μ/r1) × [√(2r2 / (r1 + r2)) - 1]
Δv2 = √(μ/r2) × [1 - √(2r1 / (r1 + r2))]
Rather than jumping directly into the station's path, modern safety guidelines mandate a co-elliptic orbit (an orbit with constant height differential below the station) to preserve a passive abort trajectory that prevents accidental re-contact even in the event of thruster failure.
4. Proximity Operations & Keep-Out Sphere
Once within 5 km, relative navigation relies on GPS differentials and optical LIDAR sensors. The spacecraft halts at designated hold points:
Approach Ellipsoid (4 km × 2 km): Formal handoff between orbital mission control and station proximity operations.
Keep-Out Sphere (200 meters): Trajectory must be verified fail-safe and passively divergent before entering.
Waypoint 2 (20 meters): Autonomous docking alignment along the IDA (International Docking Adapter) axis.
Frequently Asked Technical Questions
Why is the launch window for an orbital resupply mission instantaneous?
Because the space station travels in a fixed orbital plane inclined at 51.6 degrees, Earth's rotation carries the launch site through that orbital plane only at specific moments each day. Launching even minutes off-nominal requires massive out-of-plane steering (yaw steering), requiring excessive delta-v that severely reduces deliverable payload mass.
How does orbital phasing work during rendezvous?
By Kepler's Third Law, an orbit with a lower semi-major axis has a shorter orbital period. The chaser spacecraft is inserted into a lower circular or elliptical parking orbit (e.g. 200–300 km) where it orbits Earth faster than the station at 415 km, catching up (phasing) by several degrees every revolution until the optimal geometry for transfer burns is achieved.
What is the difference between a fast-track 4-orbit rendezvous and a nominal 24-hour profile?
A fast-track rendezvous (approx. 4 orbits / 6 hours) demands that the launch occur when the station is already in a precise angular range behind or ahead of the launch site, minimizing phasing time. A 24-to-36-hour profile allows launching into broader station positions, using multiple phasing revolutions to adjust relative distance with tighter navigational margins and lower burn stress.
How is the Earth's oblateness (J2 perturbation) accounted for?
Earth is an oblate spheroid with an equatorial bulge. This gravitational perturbation ($J_2$) causes the right ascension of the ascending node (RAAN) to precess over time. For an orbit at 51.6° inclination and 418 km altitude, the nodal precession rate is roughly -5.0° per day westward. Both the station tracking models and the launch time predictors continually compute this nodal drift to calculate exact daily liftoff times.