I see that you seem to be referring to some posts by the Institute of Creation Research. I am aware of the creationist proposal that the sun and stars are powered by gravitational collapse instead of nuclear fusion. Gravitational collapse gives the sun some of its energy, but it seems to only have enough energy to power the sun for about 20 million years. This is easy to calculate and has been done in the 1800's. But the sun is older than 20 million years. With nuclear fusion, we get e=mc^2 energy where c is the speed of light (though only a portion of the mass is converted into energy). With gravitational collapse, we get approximately (up to a small constant factor) (1/2)m v^2 energy where v is approximately the escape velocity of the surface of the sun which is about 617000 meters per second. c is about 300,000,000 meters per second. So fusion wins. Fusion gives you more energy.

Regards,

-Joseph Van Name Ph.D.