[jccc (OP)]

Light speed should be higher when it heading Earth than heading space. Vin=c+g  Vout=c-g

Am I correct? If so how easy is to examination?

If gravity works on photon, larger star light speed should be lower, small star light speed should be higher, black hole speed light is 0, so we cannot see it. Why is light speed a constant?

[PmbPhy]

Light speed should be higher when it heading Earth than heading space. Vin=c+g  Vout=c-g

This is a very serious mistake. You subtracted and added acceleration to speed. You can't do that because its meaningless. Always check to make sure that the units of the terms you're adding are the same.

Am I correct? If so how easy is to examination?

Gravity slows light but not the way you described. See
http://home.comcast.net/~peter.m.brown/gr/c_in_gfield.htm

If gravity works on photon, larger star light speed should be lower, small star light speed should be higher, black hole speed light is 0, so we cannot see it. Why is light speed a constant?

The speed of light is only invariant and constant in an inertial frame of reference. In a gravitational field where the observer is outside the field and he's measuring the speed of a photon inside the field he gets a slower speed for the light. If the observer is at the same location as the light then he gets the same thing he'd get if he was in an inertial frame though. Its the coordinate speed of light that slows down, not the locally measured speed.

[jccc (OP)]

Pete, thanks!

If 2 stars both 10 light years away, their mass ratio is 1:10^6.

2 photons from each star aim Earth at same time 10 years ago, which one first gets here? Do they have the same wave length?

[jccc (OP)]

I think the big star photon will redshift, but both photons get here at same time.

If so, redshift could cause by space expending or bigger mass, how can we make sure?

[jccc (OP)]

When star or planet mass passed a certain amount, light come from it might shift to radio wave.  Is that possible?

[PmbPhy]

Pete, thanks!

You're very welcome, buddy.  []

If 2 stars both 10 light years away, their mass ratio is 1:10^6.

2 photons from each star aim Earth at same time 10 years ago, which one first gets here? Do they have the same wave length?

First off you have to make sure that each starts from the same distance from the center of the star. When you do this and assuming that the photons have the exact same frequncy when measured locally then, ignoring the gravitational field of the earth, the one from the smaller star will get there first. As I said this is because (1) the light slows down in a gravitational field and (2) the distance is greater because gravity changes distances. When you combine these two effects you get a smaller speed for light.

Take a look at the derivation at
http://home.comcast.net/~peter.m.brown/gr/c_in_gfield.htm

Notice that in the first one the light actually goes faster as it rises. That's because its moving from a smaller gravitational potential to a greater one.

[yor_on]

I think that's a very tricky question, and the answer seem to build on your choice of coordinates when it comes to the coordinate speed of light. See https://physics.stackexchange.com/questions/399235/equivalence-principle-and-the-meaning-of-the-coordinate-speed-of-light

[yor_on]

I think I can add one thing to it. Every measurement is locally made, every observation goes out from a observer. You have to differ between 'mathematical spaces' versus locally made observations. What physics build on is not those mathematical spaces, they come later.

[Bored chemist]

I think that's a very tricky question

Is that why you took 5 years to answer?

[yor_on]

Nope :)
I still think it's a tricky question
=

It is interesting BC,, and that's what make me interested.in it.

[Bill S]

It is interesting BC,, and that's what make me interested.in it.

According to Deutsch's Law: “Every problem that is interesting is also soluble.” 

[pensador]

I think that's a very tricky question

Is that why you took 5 years to answer?

Oh that explains whty none of @PmbPhy links work any more !!!!

[yor_on]

Definitely so Bill, if we trust the chemists :)

Otherwise it's probably just a part of a whole?