[chris (OP)]

Ranjith says:

If the Sun's mass is decreasing, then the force with which sun attracts the planets (say earth) also decreases, because F = GMm/r^2 . if that happens, centripetal force decreases and centrifugal force increases and Earth slips out of its orbit. So why does it not happen?

What does everyone think?

[evan_au]

Another recent thread showed that any change in the Sun's mass (and hence Earth's orbit) is too small to measure.
You can have a theoretical calculation of some of the effects (like the average rate of hydrogen fusion), but they are too small to measure.
See: https://www.thenakedscientists.com/forum/index.php?topic=70566.msg516319#msg516319

[Janus]

Ranjith says:

If the Sun's mass is decreasing, then the force with which sun attracts the planets (say earth) also decreases, because F = GMm/r^2 . if that happens, centripetal force decreases and centrifugal force increases and Earth slips out of its orbit. So why does it not happen?

What does everyone think?

This question, by using the term "slips out of its orbit", seems to assume that orbits are narrowly defined paths around the Sun, and that if  a planet is somehow "nudged" from this path it will fly off into space or fall into the Sun.  This just isn't the case. Orbits are not the result of some fragile balance between centripetal  and centrifugal forces. Slight changes to any planet's path would just result in the planet achieving a slightly different orbit around the Sun, maybe a little closer or further from the Sun, or just a different shape.
It actually would take quite a bit to cause the Earth to either fall into the Sun or leave the solar system completely, and as odd as it may seem, it would take more to cause the former than the later.    To cause the Earth to completely leave the Solar system you would have to increase its orbital velocity by ~41% or by about 12.3 km/sec.(or at the Earth's present orbital speed, the Sun would have to lose 1/2 of its mass.).  For the Earth to fall all the way into the Sun, it would have to shed the vast majority of its nearly 30 km/sec orbital velocity.
Of course, things wouldn't have to get that extreme to have dire consequences for life on Earth,  But as pointed out, the present mass loss rate of the Sun is just too small to make a significant difference except over time scales measured in hundreds of millions of years.