How to measure the Sun's acceleration relative to the galaxy?

[KurtLudwig]

How would the acceleration of our sun relative to our galaxy be determined?
A spaceship in orbit around our sun, with engines turned off, is in free fall. Accelerometers will read zero. Turning the engines on, the accelerometers will read the acceleration due to the thrust from the engines. Measuring the distances to nearby stars, which are also moving, is tricky. Measuring the distances to stars toward the center of our galaxy, maybe the best answer. Can brightness be used to measure distances in our galaxy?

 

[PeterDonis]

How would the acceleration of our sun relative to our galaxy be determined?

The sun is in free fall, just like the spaceship you mention, so the "acceleration" you refer to is coordinate acceleration, not proper acceleration. It is much too small to be measurable directly. You can estimate what it should be from the Sun's distance from the center and orbital period or velocity around the center, which are easily found online; we can estimate those numbers fairly well from observations.

Measuring the distances to nearby stars, which are also moving, is tricky.

Actually, distances to nearby stars--near enough to get a measurable parallax--are the easiest and most accurate distance measurements we have beyond the solar system.

Can brightness be used to measure distances in our galaxy?

For certain types of stars, the "standard candles" (such as Cepheid variables) where we have an independent way to measure brightness, yes. But for most stars, we try to measure the distance and then infer the brightness (absolute magnitude) from that and the apparent magnitude.

 

[KurtLudwig]

Please correct if false or clarify: Is proper acceleration as measured by an accelerometer? Isn't coordinate acceleration a term used in relativity? Is our sun moving that fast that relativity is coming into play? According to Wikipedia, the sun travels at only 220km/s around the center of the milky way.
I understand, that there is no preferred or fixed reference position. The only constant is the speed of light. Can inertia be considered a momentary local reference frame? I still do not understand how inertia comes to be, almost as if matter is connected to other matter. An object in free fall has inertia, although its potential and kinetic energies are changing. By conservation of energy, the sum of potential and kinetic energy must stay constant, in the absence of heat dissipation. All the planets moving at different velocities have inertia. Is inertia the resistance to a change of momentum?

 

[PeterDonis]

Is proper acceleration as measured by an accelerometer?

Yes.

Isn't coordinate acceleration a term used in relativity?

Typically, but that doesn't mean it's only applicable to things moving at relativistic speeds.

Is our sun moving that fast that relativity is coming into play?

It depends on how accurate you want your predictions and measurements to be.

Can inertia be considered a momentary local reference frame?

This doesn't make sense; inertia is a property of objects, not a frame.

I still do not understand how inertia comes to be

This is a separate question which should be asked in a separate thread.

 

[Nugatory]

Is proper acceleration as measured by an accelerometer?

Yes (which means that it's trivially zero for the sun because the sun is in free-fall). But here you aren't asking how we measure the proper acceleration, you're asking for the acceleration relative to the center of the galaxy, and acceleration "relative to" something else is cooordinate acceleration - indeed, that's fairly close to being the definition of coordinate acceleration.

Isn't coordinate acceleration a term used in relativity? Is our sun moving that fast that relativity is coming into play?

The term is used in relativity, but like "speed"and "position" that's not the only place it's used. Any time you're talking about acceleration "relative to" something else, you're talking coordinate acceleration; relativity doesn't have to be involved.

And as for how we measure coordinate acceleration? We don't. We measure the distance between the accelerating object and the "relative to" point in space, and see how it changes over time.

 

[sophiecentaur]

Is inertia the resistance to a change of momentum?

Doesn't the word 'Mass' do a perfectly adequate job here - at least in Newtonian Mechanics?

Can brightness be used to measure distances in our galaxy?

Red Shift and Parallax measurements work for distances within the Galaxy. At least over the near regions in the galaxy, parallax gives fairly accurate results. Also Cepheid Variables can be used for all galactic distances (your 'brightness' idea).
I'm always gobsmacked by the accuracy of (or at least the confidence in) measurements of stellar distances and speeds.

 

[KurtLudwig]

After viewing the Milky Way, while camping in Utah, I became hooked on astronomy and cosmology. You, the advisors at Physics Forums, are lucky to have chosen this field of study. I was building machinery to manufacture cars.
Thank you for your answers.
To support Physics Forums, I will buy all books, from your website