Newton's Laws | Tale of Space

Isaac Newton (1643–1727)

Newton's Laws

The foundations of classical mechanics that govern the motion of bodies, from falling apples to orbiting planets

Principia Mathematica — 1687

Newton's laws of motion form the basis of classical mechanics. Published in 1687 in Philosophiæ Naturalis Principia Mathematica, they describe the relationship between the motion of an object and the forces acting on it. These laws explain everything from the fall of an apple to the trajectory of planets around the Sun.

Principle of Inertia

Newton's first law

If ΣF = 0 → v = constant

Without force, there is no change in motion.

In one sentence

An object at rest remains at rest, and an object in motion continues in a straight line at constant speed, as long as no force disturbs it.

Concrete examples

In space, a launched space probe continues indefinitely in a straight line without using fuel.
Your body continues to move forward when a bus brakes suddenly (hence seat belts).

Astronomical application

Asteroids travel in a straight line through space until a planet deflects them with its gravity. The Voyager probes have been continuing their interstellar journey without propulsion for decades.

Scientific Statement

In a Galilean (inertial) reference frame, a body subjected to no forces or forces whose resultant is zero remains at rest or continues in uniform linear motion.

If ΣF = 0, then v = constant (or v = 0)

Historical Background

Newton unified Galileo's work on falling bodies and Kepler's observations on planetary orbits. Before him, it was thought that motion required a continuous force (Aristotelian conception).

Validity Limits

Valid only in inertial (non-accelerated) reference frames
Approximation quand vitesses << c (vitesse de la lumière)
Does not apply to quantum scales

Technical Applications

Satellite stabilization: Conservation of angular momentum
Inertial navigation: Gyroscopes for guidance without GPS
Ion thrusters: Low continuous thrust → high speed over long periods

Fundamental Principle of Dynamics

Newton's second law

F = m × a

Force = Mass × Acceleration

In one sentence

The heavier an object is, the more force is required to move it or slow it down. The acceleration of an object is proportional to the force applied and inversely proportional to its mass.

Concrete examples

Pushing a car (1 ton) requires 100 times more force than pushing a bicycle (10 kg) to achieve the same acceleration.
Rockets must produce enormous thrust to accelerate several dozen tons.

Astronomical application

To send a probe to Mars, the force (thrust of the engines) required is calculated precisely based on the mass of the probe and the desired acceleration. It is this law that allows interplanetary trajectories to be calculated.

Scientific Statement

In a Galilean reference frame, the vector sum of the forces applied to a body is equal to the product of its inertial mass and the acceleration of its center of mass.

ΣF = m × a (vector form) Or more precisely: F = dp/dt (derivative of momentum) where p = m × v (momentum)

Key Concepts

Inertial mass: Resistance of a body to acceleration
Force: Vector quantity (magnitude + direction)
Acceleration: Change in velocity (in magnitude or direction)

Important Derivations

Conservation of momentum: if ΣF = 0, then p = constant
Kinetic energy: Ec = ½mv²
Tsiolkovsky equation: Δv = v_e × ln(m₀/m_f) — final velocity of a rocket based on the mass of propellant

Technical Applications

Ballistic trajectory calculation: Missiles, space probes
Rocket motor sizing: Thrust-to-weight ratio
Hohmann transfer orbits: Fuel-efficient orbit changes

Principle of Action-Reaction

Newton's third law

F(A→B) = −F(B→A)

For every action there is an equal and opposite reaction.

In one sentence

When object A exerts a force on object B, object B simultaneously exerts a force of equal intensity but in the opposite direction on A. These two forces act on different bodies.

Concrete examples

When you jump, your legs push the Earth down, and the Earth pushes you up.
A rocket expels gas downward → the gas pushes the rocket upward

Astronomical application

This principle is what allows rockets to function in the vacuum of space. There is no need for air to provide "support": the ejected gases create the reaction that propels the rocket. This is also the principle behind space rendezvous maneuvers (RCS).

Scientific Statement

When a body A exerts a force F(A→B) on a body B, then B simultaneously exerts a force F(B→A) on A with the same magnitude, in the same direction, but in the opposite direction.

F(A→B) = −F(B→A) Key points: • The two forces act on DIFFERENT bodies (they do not cancel each other out) • They are SIMULTANEOUS (no delay) • Valid for all interactions: gravity, electromagnetism, contact

Associated Conservation

This principle is the basis for the conservation of total momentum in an isolated system:

p(total) = constant if ΣF(ext) = 0

Technical Applications

Jet propulsion: Rockets, turbojets
Recoil of a firearm: The bullet travels forward, the weapon recoils backward.
RCS maneuvers: Reaction Control System for space rendezvous
Gravitational slingshot effect: The probe "flies" from the angular momentum to a planet.

Law of Universal Gravitation

All objects with mass attract each other. The more massive they are and the closer they are, the stronger the attraction.

F = G × (M₁ × M₂) / r²

Gravitational force between two masses

G = 6.674×10⁻¹¹

Gravitational constant (m³·kg⁻¹·s⁻²)

1/r²

Decrease with distance

∝ M₁ × M₂

Proportional to mass

What it means

The Earth attracts the Moon (which keeps it in orbit).
You attract this page with a gravitational force... but it is so weak that it is imperceptible!
The force decreases rapidly with distance (squared).

Applications

Planetary orbits: All planets around the Sun
Tides: The gravitational pull of the Moon and Sun on the oceans
Space trajectories: Gravitational assistance for probes
GPS: Relativistic corrections because gravity affects time

Full Statement

Two point masses M₁ and M₂ separated by a distance r attract each other with a force proportional to the product of their masses and inversely proportional to the square of their distance.

Gravitational Potential Energy

U = −G × (M₁ × M₂) / r (Negative because it is an attractive force; zero at infinity)

Derived Concepts

1. Kepler's third law demonstrated: T² / a³ = 4π² / (G×M_sun) = constant 2. Orbital velocity: v_orb = √(G×M / r) 3. Escape velocity: v_esc = √(2×G×M / r)

Limits and Extensions

Valable si v << c et champs gravitationnels faibles
Replaced by the General Relativity for:
- Orbit of Mercury (perihelion precession)
- Black holes (beyond the Schwarzschild radius)
- Light bending by gravity
- GPS (relativistic corrections: ±10 km/day without correction!)

Modern Applications

Newton's laws are still used daily in the space industry and modern engineering.

Rocket Launch

Calculation of the thrust required based on the total mass and target acceleration. Tsiolkovsky's equation determines the amount of fuel.

Orbits Satellites

GPS positioning, telecommunications, Earth observation—all depend on Newtonian orbit calculations.

Lunar Missions

Apollo trajectories calculated using Newton's laws. Relativistic corrections were not necessary for this distance.

Gravitational Assistance

The Voyager, Cassini, and New Horizons probes use the "gravitational slingshot" effect of planets to accelerate without fuel.

Tide Prediction

The combined gravitational pull of the Moon and Sun on the oceans makes it possible to accurately predict the tides.

Asteroid Detection

Calculation of potentially hazardous asteroid trajectories and planning of deflection missions.