PUZZLE ANSWER
If the Sun were to decrease its mass by 10% it's gravitational field would diminish. Since the Earth would still be moving around the sun at 66,000 mph, this would be too fast to maintain its current orbit and Earth would head off the orbital plane until it arrived at a distance for which 66,000 mph would keep it in orbit (and not fly off into interstellar space). Since, Earth's speed is the same but the trip around the Sun is now much farther, a year would be longer.
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