Understanding the Gravitational Dynamics

Recently, I received an intriguing question from a subscriber via email: "The Sun attracts the Moon with twice the strength of the Earth. So, why hasn’t the Moon drifted away?" This inquiry is not uncommon, and it reminded me of a similar question I addressed a few years back. Given my growing audience, I felt it was time to provide another explanation regarding celestial mechanics.

Source: earthsky.org

To assess the validity of the claim that the Sun’s gravitational pull on the Moon is twice as strong as that of the Earth, we can refer to the law of universal gravitation—a concept most of us learned in school.

Law of Universal Gravitation

By plugging in the masses of the Sun and the Moon, alongside the average distances involved, we find that the Sun indeed exerts a gravitational force on the Moon approximately 2.2 times stronger than that of the Earth. This raises a common question: why doesn’t the Sun simply pull the Moon away from the Earth? This misconception is often exploited by less scrupulous bloggers attempting to discredit universal gravitation for sensationalism.

Source: sciencelearn.org.nz

These bloggers either neglect or misunderstand celestial mechanics. For the Sun to effectively draw the Moon away from the Earth, both celestial bodies would need to be stationary relative to one another, without any external forces acting on the Earth-Sun-Moon system. Moreover, when this system originated, the bodies would have needed to possess no initial velocities or accelerations.

In reality, these conditions do not hold true. The Earth orbits the Sun just as the Moon does, and gravitational forces act on both.

To illustrate this concept, imagine you (representing Earth) are on a fast-moving train (symbolizing the Sun), and you have a cup (the Moon) on your table. The train applies a substantial force on both you and the cup, yet both experience the same acceleration. Consequently, despite the train's greater force, you can easily lift the cup and take a sip.

Source: wordpress.com

In a similar manner, we can calculate the accelerations experienced by both the Earth and the Moon due to the Sun's gravitational influence. The difference in these accelerations is so minimal compared to the force that the Earth exerts on the Moon that the Sun cannot pull the Moon away.

When viewed on a larger scale, the Moon orbits the Sun more significantly than it does the Earth. Essentially, the Earth merely retains the Moon in close proximity. If we were to hypothetically remove the Earth from the Solar System, the Moon would not head towards the Sun; instead, it would continue to orbit the Sun in the path it shared with the Earth.

In the video "Why Doesn't The Sun Steal The Moon?" we delve deeper into this fascinating topic, exploring the balance of gravitational forces and the dynamics of celestial orbits.

Furthermore, "Why the Moon Doesn't Fall to Earth" provides additional insights into the gravitational relationships within our Solar System and the mechanics that keep the Moon in its stable orbit.

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