# What (the heck) are "space-fixed coordinates" as described in Apollo mission trajectory analyses?

@Ludo's answer to If I wanted to reconstruct an entire Apollo mission's crewed spacecraft trajectories, what are the key sources of historical data I'd look for? shows the table and its source shown below.

Question: What the heck are "space-fixed coordinates"? To what in space can a coordinate system be fixed?

...table 7-II in the Apollo 11 Mission Report.

(Trajectory parameters for Apollo 11 from Apollo 11 Mission Report)

• Celestial coordinates are 'fixed' to the Sun. An ephemeris and a clock allow translating the origin to the Earth.
– amI
Dec 1 '19 at 8:55
• @amI aren't they fixed to the solar system barycenter which is usually but not always somewhere inside the Sun?
– uhoh
Dec 2 '19 at 1:09
• Note the same terminology in the Mercury documents cited in this answer: space.stackexchange.com/a/35875/6944 Dec 2 '19 at 4:04

What the heck are "space-fixed coordinates"? To what in space can a coordinate system be fixed?

That's two questions. The answer to the first is that those are Earth-centered inertial or Moon-centered inertial coordinates as indicated by the "Ref. body" column. Look at the velocities. 25600 ft/sec is orbital velocity for a vehicle in low Earth orbit while 5340 ft/sec is orbital velocity for a vehicle in low lunar orbit.

The answer to the second question is a bit more complex. One needs three orthogonal axes to form a reference system. For an inertial frame of reference, these axes should be non-rotating. The standard approach is to start with an Earth-centered point of view. One of those axes points along intersection of the Earth's equatorial plane and the ecliptic, another along either the Earth's rotational axis or along the Earth's orbital angular momentum vector, and the third completes a right handed coordinate system. Ideally, one would want these directions fixed with with respect to the "fixed" stars. However, the stars aren't "fixed" due to proper motion and parallax. The precession and nutation of the Earth's rotation axis adds another twist.

Because of precession and nutation it's important to pick a point in time to specify the orientation of the Earth's equatorial plane, and to specify how nutation was handled. This could result in mean equator and equinox of epoch, mean equator and equinox of date, true equator and equinox of date, or even something else. (GPS, for example uses "something else".) Back in the Apollo era, it was common (but not universal) to use mean equatorial coordinates referenced to the start of Besselian year 1950.0 (22:09 GMT on December 31, 1949), or M50 coordinates for short.

• – uhoh
Dec 2 '19 at 0:59
• The shuttle training simulators also used M50. Dec 2 '19 at 4:08
• @uhoh - inertial 'space-fixed' means 'star-fixed', so it is only 'body-fixed' if the body is the celestial sphere. (Nowadays the time reference for matching the Earth's pole is J2000)
– amI
Dec 2 '19 at 5:16
• @uhoh - Body-fixed coordinates rotate with the central body in question. Using those leads to the fictitious accelerations due to frame rotation. Dec 2 '19 at 13:55
• @OrganicMarble - From browsing the Apollo flight software and documents about it, it appears that that software may have used mean of NBY (Nearest Besselian Year) coordinates rather than M50. Dec 2 '19 at 14:25