Is it true? Yeah. Look, I can prove it. This is a plot of the Earth and Moon’s orbits around the Sun over half a month. The blue curve represents the Earth’s trajectory from left to right, and the red represents the moon.
Here, positions are measured in astronomical units (AU). AU was originally defined as the average distance from the Sun to the Earth. For reasons already explained, we had to use different scales on the two axes, so the trajectory looks flat. Trust me, it’s a circular orbit.
Now, let’s take a look at the moon’s orbit. First, notice that during this half-moon, the Moon starts on the other side of the Earth and ends up moving closer to the Sun (so it makes half a revolution around the Earth). Second, the moon’s path never curves away from the sun. In fact, it’s always accelerating towards solar. This is because the sun’s gravity is stronger than the Earth’s gravity.
So, again, does the moon revolve around the sun or the earth? The answer is yes. It orbits both. The moon moves around the sun, but it also moves around the earth. And it revolves around the Earth without leaving the Sun. It’s hard to visualize it in your head, but the bad news is that you can’t draw an accurate picture to help you understand.
The whole problem is that on the scale of the solar system, the Earth and Moon are so close that their relative motion is invisible. However, I am confident that textbook authors will continue their efforts.
Finally, if you still think that Earth and humanity are the center of the universe, please understand this. If our planet suddenly disappeared, the moon would only continue to orbit the sun once a year. It won’t even miss us.