It is not, which is why there isn't a solar eclipse and a lunar eclipse every 28 days. The inclination of the Moon's orbit relative to the Earth's is about 5.1 degrees.
Obviously every 14 days the Moon crosses the ecliptic (that is the plane of the Earth's orbit) and when that happens the Moon is at one of its 'nodes'. If new or full moon happens when the moon is exactly at a node, you get a solar or lunar eclipse.
The inclination explains why sometimes the moon appears to be higher or lower in the sky than the Sun ever gets.
Just to make it more tricky, the Moon's nodes rotate slowly round its orbit, getting once round in every 19 years, which is called the Metonic Cycle.
No. It's inclined about 51/2 degrees to the 'ecliptic plane' ... the plane of Earth's orbit.
If the Earth and moon orbited in the same plane, then we'd have a solar eclipse
at every New Moon, and a lunar eclipse at every Full Moon. How cool is that !
Which orbit would that be? The galactic orbit, the solar orbit, the local cluster orbit? From what viewpoint? Above or below the galactic plane, the planetary system plane, from the point of view of a different place in the local cluster than on earth itself?
gravity
they are both elliptical orbits with the earth following along a deferent (large circle) and the moon along an epicycle (small circle). the moons rotation around its axis and its revolution around the earth are the same being 27 1/3 days which is why the same lunar hemisphere always faces the earth
The moon's orbital plane is inclined about 5 degrees to the ecliptic. If the earth's and moon's orbital planes coincided, there would be a solar eclipse at every New Moon, and a lunar eclipse at every Full Moon. Pretty spectacular, but we would think that's just the way things work, and nobody would give it a second thought, like the miracle of the daily rising and setting of the sun.
The ecliptic. Because it is the plane that contains the earth as it orbits the sun, by definition it is also the plane that contains the sun as we observe it in its yearly journey through the stars.
A lunar eclipse
No. For one thing, a plane is, by definition, 2-dimensional. The moon's orbit is tilted about 5 degrees relative to Earth's orbit.
FLAT
No; it's about 23 degrees off the plane of its orbit.
The Earth's tilt, or inclination, or obliquity is about 23.44 degrees from the plane of its orbit around the Sun.
One of the results of the way gravity works is that a small body in an orbit around a large body moves in a plane. So every point in the earth's orbit around the sun is in the same plane. If you want to be perfectly technical ... the center of mass of the earth/moon system orbits the center of mass of the (sun + all the planets + all their moons) system. But the differences are so small that you can legitimately picture it as if the center of the earth orbits the center of the sun. The plane of the earth's orbit is what we call the "Ecliptic Plane". The orbits of the other planets are in close to the same plane but not exactly.
Ecliptic.
The Moon's orbit is inclined by just over 5 degrees to ecliptic plane.
1). They orbit in the same around the sun, and as the sun. 2). Orbits of planets and their larger moons are in just about the same plane. 3). Almost all planets and moons rotate on their axes in the same direction as the planets orbit the sun.
Which orbit would that be? The galactic orbit, the solar orbit, the local cluster orbit? From what viewpoint? Above or below the galactic plane, the planetary system plane, from the point of view of a different place in the local cluster than on earth itself?
The Earth orbits the Sun. The plane of the Earth's orbit is called the "ecliptic". The Moon has its own orbit around the Earth, and its own orbital plane. If the plane of the Moon's orbit was the same as the plane of the Earth's orbit, then there WOULD be solar eclipses at every new moon, and lunar eclipses at every full moon. But the plane of the Moon's orbit is NOT the same as the plane of the Earth's orbit - and really, why would they be? The Moon's orbital plane is inclined by about 5 degrees from the ecliptic. Therefore, eclipses only happen at full and new moons about every six months, when the Moon happens to be crossing the ecliptic.
That's the "ecliptic plane".