When a spacecraft departs from the International Space Station (ISS) and performs its deorbit burn, it transitions from a circular orbit to an elliptical orbit.
Now, based on your high reputation, I assume you already know how this all works, but for those of us who don't I'm going to include the process below:
Deorbit Burn:
During the deorbit burn, the spacecraft’s engines fire to reduce its velocity. This change in velocity (often denoted as ΔV or delta-V) is crucial for reentry.
The spacecraft aims to lower its altitude significantly, allowing it to reenter Earth’s atmosphere.
Elliptical Orbit:
After the deorbit burn, the spacecraft enters an elliptical orbit.
The perigee (closest point to Earth) occurs at the lowest altitude, while the apogee (farthest point from Earth) occurs at the highest altitude.
The altitude at the perigee depends on the specific mission and spacecraft design.
Typical Altitudes:
The exact altitude at the perigee varies based on mission requirements, safety considerations, and reentry profiles.
Here are some examples:
ISS Deorbit:
When the ISS is deorbited, the perigee altitude is typically lowered to around 50 kilometers (31 miles) above Earth’s surface. Source, I paraphrased
Orion MPCV (Example Calculation):
Let’s consider an example using the Orion Multi-Purpose Crew Vehicle (MPCV).
Suppose the Orion MPCV needs to change its altitude from 343.5 kilometers to 96.5 kilometers at perigee.
We can calculate the required burn time using the following steps:
Determine the change in altitude: ΔAltitude = Original Perigee - New Perigee = 343.5 km - 96.5 km = 247 km.
Use the conversion factor: 0.379 m/s² per kilometer.
Calculate the required delta-V: ΔV = ΔAltitude × 0.379 = 247 km × 0.379 m/s² = 93.613 m/s.
Apply Newton’s Second Law: F = ma, where F is force (thrust), m is mass, and a is acceleration.
Solve for acceleration: a = F / m.
Rearrange the acceleration equation to find the time required for the specific velocity change: t = ΔV / a.
Plug in the values: t = 93.613 m/s / (53,000 N / 25,848 kg) ≈ 3.34 seconds.
These values can vary based on mission specifics, spacecraft design, and operational constraints. Engineers carefully plan and execute deorbit burns to ensure safe reentry and landing.