How Newton's Laws Govern Asteroids' Motions And Impacts

Newton's laws of motion explain the relationship between a physical object and the forces acting upon it. These laws apply to all objects, including celestial bodies such as asteroids, and form the basis of modern physics. Newton's three laws of motion, together with Kepler's laws, explain why planets move in elliptical orbits rather than circles. Kepler's laws describe how planetary bodies orbit the Sun, and while asteroids obey these laws, comets do not.

Newton's First Law: Inertia

Newton's First Law, also known as the Law of Inertia, states that an object at rest will remain at rest, and an object in motion will continue moving at a constant speed and in a straight line unless it is acted on by an unbalanced force. This tendency of objects to resist changes in their state of motion is called inertia.

In simple terms, if there is no net force acting on an object, it will maintain its velocity. This means that if an object is stationary, it will stay that way, and if it is moving, it will carry on doing so in a straight line without changing speed. This is because, in the absence of any forces, there is no acceleration.

Newton's First Law applies to all objects, including asteroids. For example, an asteroid travelling through space will continue moving in a straight line at a constant speed unless it is pulled towards a larger celestial body like a planet or star, or its path is affected by another force such as a collision with another asteroid.

Newton's Law of Inertia has important implications for understanding the motion of celestial bodies. For instance, it helps explain why planets move in elliptical orbits rather than circles. It also provides insight into the forces acting on small moons and asteroids, which are not spherical like larger objects.

Newton's Second Law: Force

Newton's Second Law of Motion, also known as the Law of Force and Acceleration, states that the acceleration of an object depends on two variables: the net force acting on the object and the mass of the object. In other words, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to the object's mass. This can be expressed mathematically as:

> \(\begin{array}{l}a=\frac{F_{net}}{m}\end{array} \)

Where:

• A = acceleration
• Fnet = net force
• M = mass of the object

This equation can also be rearranged to:

> \(\begin{array}{l}F=ma\end{array} \)

Since force is a vector, Newton's second law can also be written as:

> \(\begin{array}{l}\\vec{F}=m\\vec{a}\end{array} \)

This equation shows that the direction of the total acceleration vector points in the same direction as the net force vector.

The second law is used extensively to calculate what happens in situations involving a force. For example, when kicking a ball, the force exerted in a specific direction determines how far the ball will travel. Similarly, it is easier to push an empty shopping cart than a loaded one because more mass requires more acceleration.

Newton's laws of motion, including the second law, apply to any body around any gravitational center of attraction, including asteroids.

Newton's Third Law: Action & Reaction

Newton's Third Law of Motion, often referred to as the law of 'Action and Reaction', states that whenever one object exerts a force on a second object, the second object exerts an equal and opposite reaction on the first. In other words, forces result from interactions.

This means that for every action (force) in nature, there is an equal and opposite reaction. If Object A exerts a force on Object B, Object B will exert an equal force in the opposite direction on Object A. This is often summed up in the phrase: "for every action, there is an equal and opposite reaction".

Newton's Third Law applies to all objects, including celestial bodies such as asteroids. For example, when a rocket lifts off, it pushes against the ground, and the ground pushes back with an equal force. Similarly, the force that keeps the Moon or a satellite moving along its orbit is a result of the equal and opposite reaction to the force exerted by the Earth.

• The motion of lift from an airfoil: the air is deflected downward by the airfoil, and in reaction, the wing is pushed upward.
• The motion of a spinning ball: the air is deflected to one side, and the ball reacts by moving in the opposite direction.
• The motion of a jet engine: hot exhaust gases are pushed out the back of the engine, and a thrusting force is produced in the opposite direction.

Kepler's First Law: Planetary elliptical orbits

Kepler's First Law of Planetary Motion, also known as the Law of Ellipses, states that planets move in elliptical paths around the Sun, with the Sun located at one of the foci of the ellipse. This means that the distance between the planet and the Sun is not constant; instead, it varies as the planet follows its elliptical orbit.

This law was formulated by Johannes Kepler in the early 17th century and marked a significant shift from the previously accepted notion of circular planetary orbits. Kepler's work built upon the observations of Tycho Brahe, who had extensive data on the motion of Mars. Brahe's data revealed inconsistencies with the circular orbit model proposed by Copernicus, which Kepler, his assistant, was tasked with explaining.

Kepler's First Law replaced the circular orbits of the heliocentric theory with elliptical orbits, providing a more accurate description of planetary motion. This law applies not only to planets but also to comets and moons, as demonstrated by Isaac Newton in his laws of motion and law of universal gravitation.

The discovery of Kepler's First Law was a crucial step in improving our understanding of the solar system and served as a foundation for subsequent theories and discoveries. It is worth noting that while Kepler's Law describes elliptical orbits, Newton's laws and the inclusion of gravitational forces allow for additional types of orbits, including hyperbolas and parabolas.

Kepler's Third Law: Orbital period and size

Kepler's Third Law, also known as The Law of Harmony, was formulated and published by Johannes Kepler in 1619, a decade after his first two laws of planetary motion. This law reveals the mechanics of the solar system in unprecedented detail.

The law states: "The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit." In simpler terms, the period of a planet's orbit (P) squared is equal to the size of the semi-major axis of the orbit (a) cubed when expressed in astronomical units. The equation for this is P² = a³.

This law compares the orbital period and radius of a planet's orbit to those of other planets. Unlike Kepler's first and second laws, which describe the motion characteristics of a single planet, the third law compares the motion of different planets and calculates the harmonies between them.

Thanks to this law, if we know a planet's distance from its star, we can calculate the period of its orbit and vice versa. For example, because the distance between Earth and the Sun is approximately 92,960,000 miles (or 149,600,000 kilometres) and one Earth year is 365 days, we can calculate the distance and orbital period of other planets in the solar system when only one variable is known.

As a planet's distance from the Sun increases, the time it takes to orbit the Sun increases rapidly. For instance, Mercury, the closest planet to the Sun, completes an orbit every 88 days, whereas Saturn, the sixth planet from the Sun, takes 10,759 days.

The Law of Harmony is not limited to our solar system. It has been used to calculate the orbits and masses of over 4,000 exoplanets. For exoplanets, the formula is modified to account for the variation in the star's mass compared to the Sun.

Kepler's Third Law, in combination with his second law, has also enabled astronomers to derive the masses of stars in binary systems, which is vital for understanding the structure and evolution of stars.

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