Relating to my earlier question Is it a good idea to harvest the sun to terraform Venus?
Suppose that we continue to “mine” the sun for hydrogen to be used as rocket fuel. If we continued to do so, would this begin to deplete the amount of hydrogen in the sun and start to lower it’s life expectancy, eventually causing it to explode/transform into a supergiant?
Assuming you're taking hydrogen from the surface, you'll be lengthening its lifespan.
The sun's outer convective envelope, within which hydrogen is cycled from the surface to its interior, doesn't quite reach its actively-fusing core. That core is supplied entirely by its own internal hydrogen; by the time it's done fusing into helium naturally in ~5 billion years, the outer envelope will still be hydrogen, since it won't have been cycled in.
So the only effect of removing mass from the envelope right now is to reduce the pressure on the core, and with less pressure, the core burns more slowly.
At a certain point, if you deplete the envelope by a significant margin (difficult; we're talking thousands upon thousands of Earth-masses here), you might begin to alter which parts of the Sun are convective. A low-enough mass star is fully convective and taking more mass away will simply shrink it until it can't fuse anything more at all.
As a rule of thumb, the more massive a star is, the shorter its life is.
If I remember correctly, the more massive a star is, the more densely packed are the atoms in its core and the easier it is for them to fuse, resulting in a quicker burning of the available fuel.
For a reference, you can use a calculator to estimate the life of a star based on its mass:
I doubt it. I seriously doubt it.
A long time ago in a galaxy far, far away I lived near Coeur d'Alene, Idaho. I remember watching a news broadcast about a lady who was upset because a local golf course had been given permission to draw from Lake Coeur d'Alene to water the course. She was absolutely convinced lake water levels would drop precipitously because of it and demanded that they cease and desist immediately.
Unless you're trying to fuel billions of ships a year, your civilization could realistically draw hydrogen non-stop from its star and, unless you need it to be otherwise in your story, it won't make a measurable dent in the lifespan of the star.
and if you have interstellar travel, this is even less of an issue because you could either (a) mine another star or (b) move to another solar system when your star is mined out.
I did read somewhere that by controlled removal of matter from the Sun one can make it live ~12 times its predicted lifespan while maintaining constant luminosity.
Of course, this strategy implies removing a great deal more hydrogen than the amount one would need for Venus.
On the other hand, if the goal is to teraform Venus, there are much easier sources of hydrogen available in the Solar system. E.g. the moons of Jupiter and Saturn are almost reachable as a hydrogen source even with today's technology.
