Is the prime meridian and vernal equinox direction the same?
The Earth is rotating. Representing orbits in a rotating reference frame is a complication mess, aka a PITA. What one wants is a pseudo-inertial frame of reference. Three key items are needed to accomplish this:
- A plane of reference.
Two widely used planes are the Earth's equatorial plane and the plane of the Earth's orbit about the Sun. The Earth's orientation precesses primarily due to gravitational influences from the Moon and Sun, and the Earth's orbital plane changes primarily due to gravitational influences from Jupiter and Venus. To address these changes, most people now use the mean equator at noon on January 1, 2000 or the Earth's mean orbital plane at the same point in time. ("Mean" means "average" here.)
- A sense of the normal to that plane of reference (and hence a sense of rotation).
We live in a three dimensional world. Which way is up? In the case of using the Earth's equatorial plane as the reference plane, "north" is up. In the case of using the Earth's orbital plane as the reference plane, the sense is similar: North is mostly up rather than mostly down. The unit vector pointing the this reference direction is typically denoted as $\hat z$. This is not my nomenclature. It is very standard.
- A reference direction on that plane.
Finally, reference directions on the plane are needed. Since it is highly desirable to use a right handed coordinate system, only one reference direction is needed. I'll call that direction $\hat x$. Once again, this is not my nomenclature; it is very standard. The third orthogonal direction, which is also on the reference frame, and which I'll call $\hat y$ is given by the cross product $\hat y = \hat z \times \hat x$, where $\hat z$ is "up" (see item (2) above) and $\hat x$ points toward the reference direction (this item).
A reference direction that points toward the "fixed stars" is much preferred over a reference direction that points toward the Greenwich meridian. For a very long time, astronomers saw the "fixed stars" as fixed because parallax and proper motion are very small. By the time parallax and proper motion had been observed, the term "fixed stars" was fixed, even though they're not "fixed". Nowadays, astronomers use distant quasars for establishing coordinates in space. Quasars are much closer to being "fixed" than are stars in our galaxy.