A sudden reduction in the Sun's gravity would trigger massive earthquakes on earth as we were shifted along with Earth's altered orbit. However finding something that would cause this would be very difficult! A slow reduction in gravity would mean that the earths orbit would slowly be altered. In fact what happens is the Sun's mass decreases very slightly converting it into heat and light. To put this into context the mass that the sun looses each year is about 0.25% of the sun's mass since it first was formed. Also as the Sun grows older the Sun also gets brighter which means the Earth stays warm.
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