Anyone who's been to the beach -- and seen the ocean's tides -- knows the moon's gravitational effects on Earth are rather obvious. The effects of Earth's gravitational pull on the moon are less apparent.

But a new study by scientists at NASA -- published in the journal Geophysical Research Letters -- shows even the shape of the moon's all-solid surface changes in response to the position of Earth.

"The deformation of the moon due to Earth's pull is very challenging to measure, but learning more about it gives us clues about the interior of the moon," explained Erwan Mazarico, a researcher at MIT who works at NASA's Goddard Space Flight Center.

Of course, the moon looks perfectly round in the sky. But that's because the deformation is so slight.

Mazarico and other scientists at NASA were able to pick up on the subtle changes in the moon's surface by taking extremely precise measurements using the NASA's Lunar Reconnaissance Orbiter and NASA's Gravity Recovery and Interior Laboratory, or GRAIL, mission.

Just as the moon pulls on Earth's oceans, the surface of the moon bulges slightly, rising some 20 feet in places. And as the newly collected GRAIL data showed, the position of the moon's bulge shifts over time as the angle of its orbit changes.

The gravitational relationship, as NASA describes it, is kind of like a dance -- or tug-of-war.