– Xochielt Sanchez
Answer by Robert Frost:
There is no need to define an "up" to navigate in space. But, that doesn't mean we never do. Navigation is defined according to the reference frame that is most convenient for the math and/or the visualization. I used to teach an ISS Reference Frames class, and in that class I defined around 20 reference frames that are used by the ISS for various reasons.
For objects in Earth orbit, a reference frame like M50 or J2000 or CTRS (Conventional Terrestrial Reference System) is often used.
J2000 defines its origin based on the orientation of the vectors for the Earth's rotation axis and mean vernal equinox on 1 January, 2000. At the time I wrote this answer, the ISS state vector, in the J2000 frame, was:
We mix and match a lot. We define the ISS location using J2000, but we determine that location using GPS, which provides its answer in CTRS.
In an Earth centered frame, "up" might just mean any direction radially away from the center of the Earth.
But when we talk about the orientation of the ISS, we don't use J2000, we use other frames, like LVLH (Local Vertical Local Horizontal) on the US Segment and OCK (Orbital System of Coordinates) on the Russian Segment.
And when we talk about rotations within those frames, we use Euler angles (yaw, pitch, and roll) or quaternions.
But, inside the ISS, we use body frames and those frames differ depending on whether one is in the US Segment or the Russian Segment.
If we go beyond Earth's orbit we'd switch from an Earth centered frame to a Sun centered frame.
So, "up" is very much relative, for spacecraft.