Laws Of Motion: Space Edition

The laws of motion, formulated by Sir Isaac Newton in the late 1600s, are one of the reasons he is considered the greatest scientist of all time. These laws govern the behaviour of objects in motion and their interactions with forces. But do they apply in space? After all, space is a near-vacuum with no air resistance, and gravity is relatively weak. So, do Newton's laws of motion hold up in microgravity environments, or do different rules apply?

Newton's First Law of Motion

Newton's First Law can be observed in the motion of an airplane when the pilot adjusts the throttle setting of an engine. It is also evident in the motion of a ball falling through the atmosphere, where the ball will continue falling unless acted upon by an unbalanced force, such as air resistance or gravity. Similarly, a model rocket launched into the atmosphere will continue moving in a straight line unless influenced by an external force, such as air resistance or the Earth's gravitational pull.

The law also applies to astronauts in space. For example, when Russian cosmonaut Yuri Gagarin became the first person to orbit the Earth in 1961, he experienced the practical effects of this law. When he put down his pencil while writing his log, the pencil, following the principle of uniform motion, floated out of reach. Gagarin had to complete his log by speaking into a tape recorder. Today, astronauts use Velcro or bungee straps to keep their equipment in place.

Newton's Second Law of Motion

The Second Law is particularly important for astronauts to understand, as it governs their movement in space. In the weightlessness of orbit, astronauts must learn to push themselves carefully through their spacecraft, otherwise, they will float around helplessly. They must also remember to stop themselves when they are moving towards something or someone, or they will keep going until they hit it.

The Second Law also tells us that mass and acceleration are inversely proportional. So, as mass increases, acceleration decreases, and as mass decreases, acceleration increases. For example, if a large force is applied to a small mass, it will have a large acceleration. If the same force is applied to a larger mass, the acceleration will be smaller.

Newton's Second Law can be used to calculate the new velocity and mass of an object if an external force is applied to it. This is done using the following equation:

F = (m1 x V1 – m0 x V0) / (t1 – t0)

Where:

• F = force
• M = mass
• V = velocity
• T = time

Newton's Second Law can also be thought of as a definition of force. In this interpretation, force is what exists when an inertial observer sees a body accelerating. This can be a confusing concept, as acceleration implies force, and force implies acceleration. To avoid this tautology, another statement about force must be made. For example, an equation that details the force, such as Newton's law of universal gravitation, can be inserted into the Second Law to give it predictive power.

Newton's Third Law of Motion

This law applies to a wide range of scenarios, including the motion of lift from an airfoil, where the air is deflected downward by the airfoil, and the airfoil is pushed upward in reaction. Similarly, when a spinning ball deflects air to one side, the ball moves in the opposite direction as a reaction.

Newton's third law also applies to the motion of rockets. During liftoff, hot exhaust gas is generated from fuel combustion in the rocket's engines and is pushed out of the rocket, generating thrust. For a successful launch, the amount of thrust generated must be greater than the rocket's mass.

Newton's third law played a crucial role in his argument for universal gravitation. By observing a falling apple, Newton realized that just as the Earth exerts a force on the apple, the apple also exerts an equal force on the Earth. This led him to conclude that all objects in the cosmos are interconnected through invisible chains of gravity. This insight, coupled with his laws of motion, enabled Newton to explain a wide range of phenomena, from planetary orbits to tidal cycles.

Kepler's Laws of Planetary Motion

First Law

Each planet's orbit about the Sun is an ellipse with the Sun at one of the two foci. The Sun's center is always located at one focus of the orbital ellipse, and the planet follows the ellipse in its orbit, meaning that the planet-Sun distance is constantly changing as the planet goes around its orbit.

Second Law

The imaginary line joining a planet and the Sun sweeps out equal areas during equal intervals of time as the planet orbits. This means that planets do not move with constant speed along their orbits. Their speed varies so that the line joining the centers of the Sun and the planet sweeps out equal parts of an area in equal times. The point of the planet's nearest approach to the Sun is called perihelion, and the point of greatest separation is aphelion. Thus, by Kepler's Second Law, a planet is moving fastest when it is at perihelion and slowest at aphelion.

Third Law

The squares of the orbital periods of the planets are directly proportional to the cubes of the semi-major axes of their orbits. Kepler's Third Law implies that the period for a planet to orbit the Sun increases rapidly with the radius of its orbit. For example, Mercury, the innermost planet, takes only 88 days to orbit the Sun, whereas Saturn requires 10,759 days to do the same.

Law of Universal Gravitation

The Law of Universal Gravitation, also known as Newton's Law of Gravitation, states that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. In other words, any two bodies attract each other with a force that is proportional to their masses and inversely proportional to the square of the distance between their centres. This law is represented by the equation:

> F=Gm1m2/r^2

Where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between their centres.

The law was formulated by Isaac Newton in the 17th century and published in his work "Philosophiæ Naturalis Principia Mathematica" in 1687. It was derived from empirical observations and what Newton called inductive reasoning. This publication marked the unification of previously described phenomena of gravity on Earth with known astronomical behaviours, becoming known as the "first great unification".

Newton's Law of Universal Gravitation played a crucial role in understanding the dynamics of our solar system and served as a foundation for newer theories that more accurately approximate planetary orbits. It also resembles Coulomb's law of electrical forces, which calculates the magnitude of the electrical force between two charged bodies. Both are inverse-square laws, where force is inversely proportional to the square of the distance between the bodies.

While Newton's law was later superseded by Albert Einstein's theory of general relativity, it still remains widely used as an excellent approximation of gravity's effects in most applications. Relativity is required only when extreme accuracy is needed or when dealing with very strong gravitational fields, such as those found near extremely massive and dense objects or at small distances like Mercury's orbit around the Sun.

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