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When the Moon's shadow falls on the Earth, that's called a "solar eclipse". There are two areas affected; the area of the partial eclipse, where the Moon blocks only part of the Sun, and the total eclipse, where the Moon blocks all of the Sun's light.
Because the Earth is spinning and the Moon is moving, the area of total eclipse travels across the globe from west to east. This is called the "path of totality". You can see the path of totality displayed on a Google Map for any eclipse from 2000 BCE to 3000 AD at the NASA eclipse web site at the link below.
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The point around which the Earth and Moon revolve in space is called the barycenter. It is the common center of mass of the Earth-Moon system, around which both bodies orbit due to their gravitational interaction.
First of all the Earth will cast the shadow that will hit the moon. This is why the moon looks a different color. The order of the objects is the Sun-the Earth-then the moon.
By the way the moon casts the shadow during a solar eclipse. So during a lunar eclipse, the moon doesn't cast a shadow because little to no light reach the moon to cast a shadow.
In a multi-body system like the Earth and Moon, the smaller object doesn't precisely orbit the larger one; instead, both objects orbit their "barycenter", or center of gravitational mass. If the barycenter is within the volume of the larger object, then the smaller object is a satellite. If the barycenter is outside the larger, then they are "co-planets".
In the Earth-Moon system, the barycenter is inside the Earth, so the Moon is a satellite.
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What things revolve?
Planets revolve around the sun, moons revolve around planets, and satellites revolve around Earth. Additionally, some galaxies revolve around a central point, like the Milky Way.
Does the earth revolve around the sun in a perfect circle?
No, the Earth's orbit around the Sun is not a perfect circle but an ellipse. This means that the Earth's distance from the Sun varies throughout the year, with the closest point called perihelion and the farthest point called aphelion.
What is the name for the plane in which most of the planets revolve?
The plane in which most of the planets, including Earth, revolve around the Sun is called the ecliptic plane. This plane is defined by the Earth's orbit around the Sun and serves as a reference point for the orbits of other planets in our solar system.
What way of turn does planet revolve around the sun?
All the planets revolve around the Sun in a counterclockwise (sometimes called anticlockwise) direction. To be exact, this is as viewed from an imaginary point high above the Earth's North Pole. (You actually get a different answer if you view the Solar System from above the Earth's South Pole.)
What did the program mean by the moon and earth have been dancing together for years?
The program was using a poetic metaphor to refer to the gravitational relationship between the moon and Earth, which has existed for billions of years. The moon's orbit around the Earth and its gravitational influence create a dynamic dance that has remained constant over time.
