Question

Why does a moon remain in orbit around a planet?

Short answer

A moon remains in orbit due to the balance between the gravitational force pulling it towards the planet and its tangential velocity.

Step-by-step solution

Identify the Forces Involved

To understand why a moon remains in orbit, we begin by identifying the forces at play. The primary force responsible for a moon orbiting a planet is gravity. The gravitational force is the attraction between the masses of the moon and the planet.

Gravitational Force Equation

The gravitational force can be described by Newton's Law of Universal Gravitation, which states:\[ F = \frac{G \times m_1 \times m_2}{r^2} \]where \( F \) is the gravitational force, \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses of the planet and the moon, and \( r \) is the distance between the centers of the two bodies.

Gravitational Pull and Orbit Balance

The moon is in a stable orbit because the gravitational pull by the planet provides the necessary centripetal force to keep the moon in its orbit. The gravitational force acts as an inward pull, constantly changing the direction of the moon's velocity, which keeps it moving in a circular or elliptical path.

Newton’s First Law of Motion

By Newton's First Law, an object will remain in motion unless acted upon by an outside force. The moon would fly off into space if not for the gravity that constantly pulls it towards the planet, thus acting as the 'outside force' needed to maintain the motion in orbit.

Velocity and Distance

The moon's velocity and the gravitational pull from the planet are balanced precisely. The moon’s tangential velocity is perpendicular to the gravitational pull, ensuring it doesn’t fall into the planet or escape its pull. Instead, it continually 'falls around' the planet, which creates an orbit.

Key concepts

Gravitational Force

Gravitational force is a fundamental force of nature that pulls two objects with mass towards each other. It is the reason why objects fall to the ground on Earth, and it plays a crucial role in the orbital mechanics of celestial bodies like moons and planets. The force depends on two key factors: the masses of the objects involved and the distance between them. A larger mass or a closer proximity results in a stronger gravitational force. This force keeps the moon bound to its planet, constantly pulling it towards the planet's center.

Newton's Law of Universal Gravitation

Newton's Law of Universal Gravitation is a cornerstone principle that explains how gravity operates between two masses in the universe. The law is mathematically expressed as:\[F = \frac{G \times m_1 \times m_2}{r^2}\]Here,

• \(F\) is the gravitational force,
• \(G\) is the gravitational constant,
• \(m_1\) and \(m_2\) represent the masses of the two objects (such as a planet and its moon), and
• \(r\) is the distance between the centers of these objects.

This formula demonstrates that the gravitational force grows stronger as the masses increase or the distance decreases. It provides a crucial framework for predicting and understanding the orbits of moons and planets.

Centripetal Force

Centripetal force is the "center-seeking" force required to keep an object moving in a circular path. Without this force, an object would travel in a straight line due to its inertia. In the case of a moon orbiting a planet, the gravitational force acting between the two bodies provides this necessary centripetal force.
Gravitational force constantly pulls the moon towards the planet, altering its straight line motion into a curved one and maintaining the moon's orbit. This interplay ensures the moon remains in a stable path around the planet, effectively following a circular or elliptical trajectory.

Newton's First Law of Motion

Newton's First Law of Motion, often cited as the "law of inertia," states that an object will continue in its state of rest or uniform motion unless acted upon by an external force. In orbital mechanics, this law explains why a moon, without the gravitational pull from its planet, would drift off into space in a straight line.
However, the gravitational attraction acts as this external force that alters the moon's linear trajectory into an orbit. This delicate balance of tangential velocity and gravitational force ensures the moon perpetually "falls" around the planet, maintaining its orbit without crashing into the planet or escaping its gravitational pull.