Inertial frames and fixed stars

Question

How did newton take fixed stars as inertial frames of reference in his definition of inertial frame? If anyone knows the logic then please help me.

Answer 1

Note: Neither the concept of absolute space nor of the Newtonian inertial frame are in current use. An inertial frame is one with a proper acceleration of 0. (Proper acceleration is what an accelerometer measures.) There is no absolute space with a privileged rest frame. The below is a statement about 17th century ideas, not a statement about the nature of the physical universe.

---

"Fixed stars" are/were the little specks of light you see if you look up at night that don't wander around (that is, excluding comets, planets, and, in the modern era, man-made satellites). Most educated people through history before the invention of electric lights would be at least passingly familiar with the movements of the heavens. They would thus know that all heavenly bodies except for comets, shooting stars, the Sun, the Moon, and the five$^a$ planets are fixed with respect to all the others, rotating along the ecliptic in unison with the day, and shifting along the zodiac in unison with the year.

Newton posits the existence of "absolute space" - but notes that there's no way for anyone to measure what an object's velocity with respect to absolute space is, because all inertial bodies look like they're stationary if you're comoving with them. A Newtonian inertial frame is one which is in uniform linear motion with respect to absolute space; that is, one for which net force (counting gravity as a real force) equals zero. You can't tell what absolute space is, but you can tell what uniform linear motion is if you look around and a bunch of things seem to move in unison.

The fixed stars are a bunch of things that seem to move in unison.

Therefore the fixed stars are almost certainly in uniform linear motion (within the limits of 17th century measurement) with respect to "absolute space", and hence constitute one inertial reference frame.

Because all Newtonian inertial bodies are in uniform linear motion with respect to all other Newtonian inertial bodies, any body which is in uniform linear motion with respect to the fixed stars is inertial in the Newtonian sense.

a: Mercury, Venus, Mars, Jupiter, and Saturn are visible to the naked eye.

Answer 2

In astronomy: as long as there has been astronomy the motion of the moving celestial objects (the Sun, the Moon, the planets, and the occasional comet) was taken as motion relative to the fixed stars.

For Newton to use anything other than the fixed stars as reference would have been a choice, a choice that would require reasons to make that choice.

Kepler's three laws of celestial motion are applicable for motion with respect to the fixed stars. Again, that was not a particular choice, Kepler simply used the convention of centuries: to use the fixed stars as the reference of motion of the moving celestial bodies.

If you use anything other than the fixed stars then you will fail to find any laws of celestial motion. Kepler's laws of celestial motion obtain if and only if you use the motion of the planets relative to the fixed stars.

Thought experiment

What if some Galactic event would cause a star and its planets to depart from its parent galaxy, and careen into inter-galactic space.

(In galaxy-galaxy interaction: a tidal event can cause a stream of material to depart from its parent galaxy. A star and its planets can be part of such a stream. Such an event is not violent; the star will retain its planets.)

Let's say a runaway star and its planets move to inter-galactic space in that way. After several billions of years the runaway star can be so far away from all surrounding galaxies that none of them is visible to the naked eye.

Under those circumstances: is it still possible for a Kepler to arrive at Kepler's laws of celestial motion?

I submit that the answer is Yes.
For the astronomers of a planet orbiting a runaway star the Kepler problem will be significantly harder, but not impossible.

There is the plane of the orbit of the Earth, the orientation of that plane is fixed. There is also that plane of the Earth's equator. That plane is not quite fixed, since the equatorial plane moves with the precession of the equinoxes, but that motion is very slow; within the lifetime of any astronomer the precession of the equinoxes is imperceptible.

Take the line of intersection of the Earth's orbital plane and the plane of the equator. Use that line to define the zero point of the reference for planetary motion.

For the motions of the planets relative to that reference we have that Kepler's laws of motion will obtain. Over time, as the calculations become more accurate the astronomers will suss out that the plane of the equator is actually moving. At that point the astronomers will move to the following definition of reference for the motions of the planets. There is a single reference that has the property that the laws of celestial motion obtain. (Kepler's laws, and later: the inverse square law of gravity) The reference with the property that the laws of motion obtain is the appropriate reference.

My reason for submitting that thought experiment:
Historically the fact that the fixed stars are available was very helpful; the fixed stars provide a natural reference. The motion with respect to the fixed stars is the motion for which laws of celestial motion obtain. However, having fixed stars visible is not an absolute necessity.

Without visible fixed stars the Kepler problem would have been much harder, but by no means impossible.