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Navigating in orbit usually relies on firing engines for some amount of time to achieve a specific velocity. This answer, for example, mentions "closed-loop guidance" for the ISS boosting.

  1. How is the initial velocity of the spacecraft usually measured? Is it estimated from the known orbital parameters? Is it corrected for perturbations and drag, in the case of LEO?
  2. How is initial attitude measured? Is a star tracker used, or other optical measurements from the spacecraft? Or is it mostly ground-based?
  3. How is the ongoing change in velocity measured? I suspect a IMU is only part of the answer here, due to integration errors?

Notes:

I'm mostly interested in both stable orbits and transfer orbits around earth and other bodies, not so much the initial launch (which is tracked from ground based radar, as I understand?)

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This is how it worked for the Space Shuttle, it was fairly autonomous.

enter image description here

To perform insertion, orbit, and deorbit maneuvers, there must be accurate data for the orbiter's location and velocity with respect to the Earth for use by guidance and control. This is the task of the shuttle navigation software. The navigation software maintains an accurate estimate of the orbiter’s inertial position and velocity in the form of a seven-element “state vector.”

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During accelerated flight, the IMUs supply the information to calculate this vector. The onboard vector may be updated or replaced by the ground with a vector based on data obtained from tracking devices.

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Because the vehicle's location changes with respect to the Earth as it orbits, the state vector is constantly changing, and nav is continually having to recompute it. This is done in the General Purpose Computers (GPCs) via an algorithm known as “super-g navigation.”

The Super-g Algorithm performs the following functions:

a. Given the state vector and gravitational acceleration from the last cycle, a new position vector is estimated using either modeled drag acceleration or IMU-sensed acceleration.

b. The gravity at the new position is calculated.

c. Using the change in gravity from the past to the current cycle, the position and velocity vectors are recomputed.

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The flight controllers in the Mission Control Center (MCC) have the capability to monitor the onboard state vector as computed by nav. In addition, they can monitor tracking data from ground-based radar and other external sources. By comparing the two, they can see what sort of errors are accumulating. Errors in the onboard state vector are inherent in the propagation scheme and grow with time, following a fairly predictable pattern. MCC evaluates these errors and may uplink a correction factor called a “delta state update” (if in powered flight) or a new state vector (if in coasting flight) into the system.

IMU - Inertial Measurement Unit

Everything from Guidance and Control Insertion/Orbit/Deorbit Workbook (not currently online AFAIK)

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