Why don't we see solar and lunar eclipses every lunar cycle?


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Answer:
We don't see solar and lunar eclipses every lunar cycle because the Moon's orbit doesn't lie in the Earth's orbital plane around the Sun. If it did so, there would indeed be one solar and one lunar eclipse every "lunar cycle" or month.

In fact, the plane of the Moon's orbit is "tilted" at an angle of about 5 degrees to the Earth's orbital plane. That's sufficiently large so that most months, as seen from the Earth, the Moon passes above or below the Sun when it's otherwise seen "in the Sun's direction." (Similarly, the Moon passes below or above the shadow that the Sun is casting of the Earth out into space.)

Only around two times a year, separated by about 6 months, are the Sun, Earth and moon "line-ups" suitable for creating eclipse effects (full, partial, annular, ...). These parts of the year are called the "eclipse seasons."

Actually, if you examine the dates eclipses of any kind occur in successive years, you find that both eclipse seasons slowly slip forwrad in their dates in those years. Yet still the tilt of the Moon's orbit remains at about 5 degrees. That means that the Moon's orbital plane isn't staying in the same place from year to year. Instead, it's slowly slipping around, keeping the same 5 degree "tilt angle," but moving all the way around the entire 360 degrees of the sky in about 18.6 years. This is called the "precession of the Moon's orbital plane." It's analogous to the effect you'll see if you try to balance a rapidly spinning bicycle wheel on your finger. It's also similar to the precession you can observe in toy gyroscopes, slightly tilted over out of the vertical.

This lunar orbital precesion was known to the ancients. Using it, they could not only predict when eclipses WOULD occur, but also what the character of different sets of successive eclipses would be. That must have seemed like MAGIC to some of their awed contemporaries!

Lunar orbital precession is largely caused by the Sun, steadily tugging gravitationally on the Moon as it orbits around the Earth. (There's a less important contribution from the pull by the Earth's equatorial bulge.) That tuggging creates a torque on the dynamical spin properties of the Moon's orbit, just like it's a torque from the weight of a tipped over, rapidly spinning bicycle wheel, or a spinning gyroscope (both held at an angle to the vertical), that makes them precess.

You need good three dimensional visualization skills to appreciate all these effects.

I hope this has helped you.

Live long and prosper.
Because the orbits are not perfectly round, and the earth tilts back and forth (wobbles) on it's axis, causing teh changing seasons, so we don't always have the same view.
Because the moon is tipped at an angle of about 5 degrees one way or the other to the plane of the earth and sun - so it only gets in the way twice a year as it's orbital plane tips.
The orbits of the Earth, Moon, and Sun are not exactly coplanar. The Moon does cross in front of the Sun and behind the Earth occasionally, but the majority of the time it does not.
all the three sufaces ( the earth on which we are standing and lookint at the eclipse, the moon, and the sun whose rays are falling on the moon and illuminating it.) are revolving not only on its axis but also arround other object.
like earth is revolving arround sun, the moon is revolving arround earth and the whole milky way galaxy is revolving . all these revolving makes it impossible that all the three objects are in the same position on every lunar cycycle.
The orbit of the Moon is inclined 5° to the ecliptic. The Sun and Moon both have an angular diameter of about 0.5°, which means they have to be within 1° of each other when "aligned" for one to even partially eclipse the other.
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