Moon 

The Moon is Earth's sole natural satellite and one of the most captivating objects in the night sky. Its existence has strongly affected Earth's tides, calendar systems, and even cultural myths and legends.

1.0Introduction 

The Moon is Earth's natural satellite, with an average distance of around 384,400 Km from Earth. Centuries ago, the Moon had been a topic of study in science. Understanding the Moon is crucial for many physics ideas, such as gravity, motion, and energy. For these reasons, its interaction with Earth's tides and its phases gives very fundamental lessons in classical mechanics and gravitation.

Gravity on the Moon 

The value of “g” on the Moon or acceleration due to gravity on the Moon is less than on the Earth. The Gravitational acceleration (g) of the Moon is almost 1/6th of the Earth’s gravity. (the value of “g” on Earth is 9.8m/s^2, meaning it will be 1.625m/s² on the moon). This makes objects on the Moon weigh only one-sixth of what they would weigh on Earth. In other words, if on Earth something weighed 60 kg, it would only weigh 10 kg on the Moon. This is just because the mass of the Moon is far smaller compared to Earth as well as its size is much less than Earth.

The Phases of the Moon 

As seen from the Earth, the Moon undergoes different phases that are basically the different shapes of the Moon, repeating itself every 29.5 days. The cause of these phases is the changing position of the moon related to Earth and the sun. The main phases of the moon include: 

New Moon:  The New Moon is the beginning of the Moon’s cycle. In this phase, the Moon positions itself in between the Earth and the Moon, hence, the side of the Moon that faces the Earth becomes Invisible.
Waxing Crescent:  After the New Moon, on the right side of the moon, a small illumination of the Moon can be seen, known as the Waxing Crescent Phase.
First Quarter:  In this phase, half of the Moon is illuminated after a week of the New Moon. The Moon completes a quarter of the cycle around Earth in this phase.
Waxing Gibbous:  More than half of the Moon is illuminated in this phase. The Brightness of the Moon increases as it reaches the full Moon stage.
Full Moon:  When the Moon faces Earth and is illuminated by the sun, the full Moon is seen. In this Phase, the Earth comes in between the Moon and the Sun, hence the Moon reaches the opposite of the Sun.
Waning Gibbous:  After the full Moon, the illumination of the Moon begins to decrease. In the waning Gibbous phase of the Moon cycle, more than half of the Moon still remains illuminated.
Last Quarter:  This phase is similar to the First quarter phase of the Moon, but in this case, the left side of the Moon is illuminated.
Waning Crescent:  In this phase, only a small silver illuminated part is seen on the left side of the Moon, and from here, the Moon continues to shrink further until it again reaches the new Moon phase.

2.0Why doesn’t the Moon Fall into the Earth? 

The answer to this question lies within the Moon’s orbital motion and the balance between gravitational force and centripetal force.

• We know that the Moon is constantly being pulled by the Earth, but the Moon is also pulling the Earth with equal and opposite forces, besides, the Moon also has a forward velocity in its orbit around Earth. This forward velocity propels the moon in a curved path rather than falling straight toward Earth. Essentially, the Moon is in free fall, but because it is moving forward at a high speed, it continuously "misses" the Earth.
• Gravitational Attraction and Centripetal Force: The gravitational pull of Earth to the Moon is what makes it move within an orbit by providing its centripetal force. If there were to be a loss of forward velocity(orbital velocity) of the Moon, it would continue falling towards Earth. If the gravitational pull of Earth were to dissolve, the Moon would just continue in a straight line tangent to its orbit. 
• The centripetal force required to keep the Moon in orbit can be calculated using the formula:

$F=Mmv2r$

Where:

• M_m is the mass of the Moon,
• v is the orbital velocity of the Moon,
• r is the distance between the Moon and Earth.

3.0Effects of the Moon on Earth

• Tides: 

The most common and known effect of the Moon is the tides. The gravitational force of the Moon pulls the oceans of Earth due to which the oceans bulge, creating high and low tides. The Sun also affects the tides but due to the Moon being closer to Earth, it has more effect on Earth’s Oceans than the sun. 

• Stabilization of Earth’s axis: 

The Moon helps stabilize Earth's axial tilt, which is responsible for our seasons. Without the Moon, Earth's axis could wobble more, leading to extreme climate shifts.

• Extension of Day:

The gravitational interaction between Earth and the Moon slows Earth's rate of rotation gradually, producing tidal friction. In that way, the length of a day on Earth gets longer.