Answer:
If, by some magical event, the moon could be suddenly gone from its orbit around the Earth there would be no noticeable effect on the Sun. However, there would be some immediate effects and some long term effects on the Earth. Besides the obvious changes of no longer seeing the Moon’s various phases and the occasional eclipses, in the short term, the ocean tides would be greatly reduced. The ocean tides are due to the effects of a gradient in the gravitational field due to both the moon and the sun. However, the moon makes a greater contribution to the tides than the sun, despite the fact that its total gravitational force is weaker than the Sun’s, the gradient of the Moon’s gravity (i.e. difference in gravitational force on the near and far sides of the Earth from the Moon) is greater than the gradient in the Sun’s force. It is the gradient of gravitational force that causes tides. Thus the tides from the Sun are weaker. Besides weaker tides, the monthly cycle of so called spring tides and neap tides would go away. Spring tides (the strongest tides) occur at full and new moon phases when the Earth, Moon and Sun are nearly in a line, and the neap tides (the weakest tides) occur at the first and third quarter moon phase, when the moon is pulling on the oceans at right angles to the pull from the Sun’s gravity.
In the long term over millions of years, there would be a number of effects, some of which I’ll highlight here. Since the Moon helps stabilize the angle of tilt of Earth’s spin axis, which in turn stabilizes our seasons, we could have huge shifts in our seasons and length of day/night, even to the point that the north and south poles could point directly at Sun over the course of a year. This would produce extreme seasons where for example, the United States would have daylight lasting several months in which the Sun would never be above the horizon, plunging us into very deep cold worse than the south pole in winter. Similarly, we’d have several months at a time where the Sun never sets, baking us and evaporating many lakes and rivers. Life as we know it wouldn’t be possible for most creatures, though bacteria, algae and some protected plant seeds and burrowing animals might survive, though I’m speculating here (not a biologist).
Another minor effect that comes to mind is the Earth’s rate of rotation, which is slowly decreasing, would not be slowing as fast, since the slowing of our spin rate is a result of tidal drag, with the biggest contribution from the moon.
This is not a exhaustive list, but I hope it gives some idea of the role played by the Moon.
Explanation:
