The Physics of Orbits: Why the Moon Doesn't Fall, Satellites Stay Up, and Astronauts Only Look Weightless

Falling and Missing

Here’s a question that sounds stupid but leads somewhere profound: why doesn’t the Moon fall down?

It’s up there, roughly 384,000 kilometres away, and Earth’s gravity is definitely pulling on it. The force is enormous — about 2 × 10²⁰ newtons, enough to accelerate the Moon toward Earth at about 2.7 millimetres per second every second. And yet the Moon doesn’t crash into Earth. It just goes around and around, and has been doing so for about 4.5 billion years.

The answer — which Newton worked out in the 1680s and which changed humanity’s understanding of the cosmos — is that the Moon is falling. It’s falling right now. It never stops falling. But it’s also moving sideways, and it’s moving sideways fast enough that by the time it’s fallen a certain distance toward Earth, the curved surface of Earth has receded by the same amount.

The Moon falls but never hits the ground, because the ground keeps curving away.

That’s an orbit. Not floating. Not hovering. Not defying gravity. Just falling, perpetually, around a curve.

Newton’s Cannonball: The Thought Experiment That Explains Everything

Newton illustrated this with a thought experiment that remains, I think, the best way to understand orbits.

Imagine a cannon mounted on top of an absurdly tall mountain — tall enough to poke above the atmosphere (so we can ignore air resistance). Fire the cannon horizontally. The cannonball arcs downward and hits the ground some distance away. Normal ballistics.

Now fire with more gunpowder. The cannonball travels farther before hitting the ground. But Earth is round, and the surface curves away from a straight line. With enough velocity, the cannonball travels so far that the drop in its trajectory exactly matches the curvature of the Earth. It falls toward Earth, but Earth’s surface falls away beneath it at the same rate. The cannonball goes all the way around and comes back to its starting point.

That’s orbit. The cannonball is in a state of continuous free fall — gravity is the only force acting on it — but its sideways velocity prevents it from ever reaching the surface. No engine needed. No fuel. Once you’re at orbital speed, you stay in orbit indefinitely (ignoring atmospheric drag, which we’ll get to).

The speed required depends on how high you are. At 200 kilometres altitude — the edge of practical low Earth orbit — you need about 7.8 kilometres per second of horizontal velocity. That’s 28,000 km/h. Mach 23. Nearly twenty times faster than a rifle bullet. Getting to that speed is what makes spaceflight so expensive. Not the altitude — a 200-km altitude could be reached with a modest sounding rocket. It’s the velocity that costs you. Most of a rocket’s fuel is spent accelerating sideways, not going up.

Kepler Got There First (Sort Of)

About 70 years before Newton, Johannes Kepler deduced the shape and timing of orbits from Tycho Brahe’s painstakingly precise observations of Mars. Kepler didn’t know why planets moved the way they did — he had no theory of gravity — but his three laws described the motion with remarkable accuracy.

Kepler’s first law: Every planet moves in an ellipse with the Sun at one focus. Not a circle — an ellipse. The circle is just a special case (an ellipse with zero eccentricity). Most planetary orbits are nearly circular, but comets can have eccentricities close to 1, swinging in close to the Sun and then retreating to the outer reaches of the solar system.

Kepler’s second law: A line drawn from the Sun to a planet sweeps out equal areas in equal times. This means planets move faster when they’re closer to the Sun (near perihelion) and slower when they’re farther away (near aphelion). Earth is about 3.3% closer to the Sun in January than in July, and it moves about 3.3% faster. You’re orbiting the Sun faster in winter (if you’re in the northern hemisphere) than in summer.

Kepler’s third law: The square of the orbital period is proportional to the cube of the semi-major axis. T² ∝ a³. This is the law that locks orbital altitude to orbital period. It’s why there’s exactly one altitude for a 24-hour orbit (geostationary), one for a 90-minute orbit (low Earth orbit), and one for a 27.3-day orbit (the Moon’s distance). You can’t choose altitude and period independently — nature sets the relationship.

Newton’s triumph was showing that all three of Kepler’s laws follow from a single assumption: a gravitational force that acts between any two masses, proportional to the product of their masses and inversely proportional to the square of the distance between them. F = GMm/r². One equation, and Kepler’s empirical laws fall out as mathematical consequences. Along with the orbit of every moon, every planet, every binary star, and every galaxy.

I think this is one of the most beautiful moments in the history of science. Kepler spent years extracting patterns from data. Newton derived those patterns from a single physical principle. The universe turned out to be simpler than the observations suggested.

The Weightlessness Illusion

Astronauts on the International Space Station float. They tumble. Their hair stands on end. Water forms perfect spheres. Everything about it screams “zero gravity.”

But there’s a problem: the ISS orbits at about 400 kilometres altitude, and at that height, Earth’s gravitational pull is about 8.7 m/s² — roughly 89% of its surface value (9.8 m/s²). The astronauts are not beyond gravity’s reach. They’re not even close. Gravity up there is almost as strong as gravity down here.

So why do they float?

Because they’re falling. The ISS, the astronauts, the equipment, the water — everything is falling toward Earth together, at the same rate. Inside the station, there is no relative motion between the astronaut and the floor. The floor doesn’t push up on the astronaut because the floor is falling too. No push means no sensation of weight.

It’s exactly the same physics as a free-falling elevator. If you were in an elevator and the cable snapped, you would float — briefly, terrifyingly — because you and the elevator are both accelerating downward at 9.8 m/s², and there’s no contact force between you and the floor. The ISS is a falling elevator that never reaches the ground.

Einstein made this insight the foundation of general relativity. He called it the happiest thought of his life: a person in free fall feels no gravity. Free fall and weightlessness are locally indistinguishable from floating in deep space, far from any massive object. This equivalence principle — that gravity and acceleration are locally the same — is the conceptual cornerstone of Einstein’s theory of relativity.

The proper term for conditions on the ISS is microgravity, not zero gravity. There are tiny residual accelerations from atmospheric drag (the ISS ploughs through a thin wisp of atmosphere at 400 km), tidal forces (different parts of the station are at slightly different distances from Earth), and the station’s own rotation. These residual forces are on the order of 10⁻⁶ g — a millionth of surface gravity. Small enough to float, but not exactly zero.

Orbital Mechanics: The Counterintuitive Art

Orbital mechanics is famously counterintuitive. Your instincts from driving a car or riding a bicycle fail completely. Here are some of the ways orbits confuse people — and the physics behind them.

To speed up, you slow down. An object in a low orbit moves faster than an object in a high orbit. The ISS at 400 km altitude zips along at 7.66 km/s. A GPS satellite at 20,200 km altitude moves at only 3.87 km/s. The Moon at 384,000 km crawls at 1.02 km/s. The lower you are, the faster you go. If you want to catch a satellite ahead of you in the same orbit, firing your engines forward (to speed up) will actually push you to a higher orbit where you move slower. To catch up, you need to fire backward — dropping to a lower, faster orbit.

To go up, you go sideways. Orbits are changed by burning prograde (in the direction of travel) or retrograde (against the direction of travel). A prograde burn at one point in your orbit raises the altitude on the opposite side. A retrograde burn lowers it. You don’t point your rocket “up” to go higher — you point it forward, along your orbital path. The vertical component is handled automatically by the changed orbital shape.

There are no brakes. In a vacuum, an orbiting object keeps orbiting forever. There’s no friction, no air resistance (at high altitudes), nothing to slow you down. This is wonderful for satellites that need to stay in orbit, and terrible for space debris. A dropped wrench, a paint fleck, a dead satellite — they all keep orbiting at 7+ km/s until something changes their trajectory. At those speeds, even tiny objects carry enormous kinetic energy. A 1-centimetre paint fleck at orbital velocity has roughly the kinetic energy of a bowling ball travelling at 100 km/h.

Rendezvous is absurdly difficult. Bringing two spacecraft together in orbit — as in docking with the ISS — is one of the most complex manoeuvres in spaceflight. You can’t just point at the target and fire. Every burn changes your orbit shape, period, and phase simultaneously. The Gemini programme in the 1960s was dedicated largely to mastering orbital rendezvous, and even experienced engineers found it deeply unintuitive.

Types of Orbits

Not all orbits are equal. The choice of orbit depends on the mission, and each orbit type has distinctive physics.

Low Earth Orbit (LEO): 200–2,000 km altitude. Period: about 90 minutes to 2 hours. This is where the ISS, most Earth observation satellites, and the Hubble Space Telescope operate. LEO is easy to reach (relatively speaking) and provides close-up views of Earth’s surface, but satellites must move fast (7.5–7.8 km/s) and each orbit covers only a strip of the planet. At the lower end, residual atmospheric drag is significant — the ISS loses about 2 km of altitude per month and needs periodic re-boosts.

Medium Earth Orbit (MEO): 2,000–35,786 km. The GPS constellation operates here, at about 20,200 km altitude with a 12-hour period. This means each GPS satellite completes exactly two orbits per day, and the constellation geometry repeats daily — useful for navigation accuracy. MEO is also home to the Galileo (EU) and BeiDou (China) navigation systems.

Geostationary Orbit (GEO): 35,786 km above the equator. Period: exactly 24 hours, synchronised with Earth’s rotation. A satellite here appears motionless from the ground, making it ideal for communications (satellite TV, satellite internet) and weather observation. But there’s only one geostationary ring, and it’s getting crowded — over 500 active satellites share this unique altitude, spaced about 0.1° apart (roughly 75 km separation).

Sun-synchronous Orbit (SSO): A polar orbit (passing over both poles) at about 600–800 km altitude, tilted so that the orbital plane precesses at exactly the rate needed to keep a constant angle relative to the Sun. This means the satellite crosses each latitude at the same local solar time every orbit — always seeing a location at, say, 10:30 AM local time. This consistent lighting is essential for Earth observation and environmental monitoring, where you need to compare images taken at different dates under similar illumination.

Highly Elliptical Orbits: Some missions require orbits that are far from circular. The Molniya orbit (used by Russian communications satellites) has a 12-hour period with an apogee of about 40,000 km over the northern hemisphere and a perigee of only about 500 km over the southern hemisphere. The satellite spends most of its time near apogee (Kepler’s second law — it moves slowly when far from Earth), providing extended coverage of high northern latitudes that geostationary satellites can’t serve well because they’re always above the equator.

Escape Velocity: The Price of Leaving

There’s a speed above which an object will never come back. Fire Newton’s cannonball fast enough and instead of orbiting, it flies away from Earth on a hyperbolic trajectory, slowing down but never quite stopping, never turning around.

This threshold is the escape velocity, and for Earth’s surface it’s about 11.2 kilometres per second — roughly 40,000 km/h. It’s not a matter of direction — escape velocity is a scalar, not a vector. If you have that speed in any direction (ignoring the atmosphere), you’ll escape Earth’s gravity.

The physics is energy conservation. An object with kinetic energy equal to or greater than the (negative) gravitational potential energy is unbound — it has enough energy to reach infinity with zero or positive velocity remaining. The escape velocity is simply:

v_escape = √(2GM/r)

where G is the gravitational constant, M is the mass of the body, and r is the distance from its centre. For Earth’s surface (M = 5.97 × 10²⁴ kg, r = 6,371 km), you get 11.2 km/s. For the Moon’s surface (smaller M, smaller r), it’s only 2.4 km/s. For the Sun’s surface, it’s 618 km/s.

The escape velocity from the surface of a black hole exceeds the speed of light. That, in fact, is what defines the event horizon — the surface at which escape velocity equals c. Nothing escapes, because nothing can travel at the speed of light.

Every interplanetary mission — to Mars, Jupiter, the outer planets — must first achieve Earth’s escape velocity (or something close to it). This is why interplanetary missions need larger rockets than those used for Earth orbit. Getting to orbit costs you 7.8 km/s. Leaving Earth entirely costs you 11.2 km/s. That extra 3.4 km/s, because of the exponential nature of the rocket equation, requires enormously more fuel.

Lagrange Points: Where Forces Balance

In the gravitational field of two large bodies orbiting each other — the Sun and Earth, Earth and Moon — there are five special positions where a small object can remain stationary relative to both bodies. These are the Lagrange points, calculated by Joseph-Louis Lagrange in 1772.

L1 sits between the two bodies. The Sun-Earth L1 is about 1.5 million kilometres from Earth, toward the Sun. Here, the Sun’s gravity is partially cancelled by Earth’s gravity, and the object orbits the Sun with a period of exactly one year (matching Earth) despite being closer to the Sun. The SOHO and DSCOVR solar observatories sit near L1, providing an unobstructed view of the Sun.

L2 is beyond the smaller body, on the opposite side from the larger one. The Sun-Earth L2 is about 1.5 million km from Earth, away from the Sun. The James Webb Space Telescope orbits around L2, where it can keep the Sun, Earth, and Moon all behind its sunshield simultaneously, maintaining the extreme cold its infrared detectors require.

L3 is on the far side of the larger body — for the Sun-Earth system, it’s on the opposite side of the Sun from Earth. It has no current practical use and is unstable.

L4 and L5 are the fascinating ones. They’re located 60° ahead of and behind the smaller body in its orbit, forming equilateral triangles with the two large bodies. Unlike L1, L2, and L3, which are unstable (objects placed there will drift away without station-keeping), L4 and L5 are genuinely stable — objects near them oscillate around the point rather than drifting away. This stability is why Jupiter’s L4 and L5 points are home to the Trojan asteroids — over 12,000 known objects that have been gravitationally trapped there for billions of years.

The physics of Lagrange points is a beautiful example of how complicated behaviour emerges from simple laws. There’s nothing special about these locations — no force field, no barrier. It’s just that the combination of gravitational pulls and the centrifugal effect of orbital motion happen to cancel in exactly five places. Mathematics picks out special solutions that intuition would never find.

Orbital Decay and the Problem of Space Junk

Low orbits aren’t permanent. Even at 400 km altitude, there’s enough residual atmosphere to create drag on orbiting objects. The atmosphere doesn’t end abruptly — it tapers off exponentially, and at 400 km there are still roughly 10⁸ gas molecules per cubic centimetre (compared to 10¹⁹ at sea level). That’s an extraordinarily good vacuum by terrestrial standards, but at orbital velocities, those rare molecules add up.

The ISS experiences a drag force equivalent to about 0.1 newtons — a force you could resist with your little finger. But there’s no opposing thrust (most of the time), so this tiny force gradually saps orbital energy. The ISS drops about 2 km per month and needs regular re-boosts from visiting cargo spacecraft or its own engines. Without them, it would re-enter the atmosphere in roughly 12 to 18 months.

Above about 1,000 km, atmospheric drag becomes negligible, and objects orbit for centuries or millennia. This is the space debris problem. Since the dawn of the space age, we’ve left behind spent rocket stages, dead satellites, tools dropped by astronauts, fragments from collisions and explosions — currently over 36,000 tracked objects larger than 10 cm, hundreds of thousands between 1 and 10 cm, and possibly hundreds of millions below 1 cm.

At orbital velocities, debris impacts are catastrophic. The kinetic energy of a collision at 10 km/s goes as ½mv². A 1-cm aluminium sphere at that speed carries about 6,500 joules — comparable to a hand grenade. And each collision creates more debris, which can cause more collisions, in a runaway chain reaction called the Kessler syndrome, predicted by NASA scientist Donald Kessler in 1978.

This isn’t a hypothetical scenario. In 2009, the active communications satellite Iridium 33 collided with the defunct Russian military satellite Cosmos 2251 at roughly 11.7 km/s, generating over 2,000 trackable fragments that remain in orbit today. China’s 2007 anti-satellite missile test deliberately destroyed a defunct weather satellite and created over 3,500 trackable pieces of debris — the single worst debris-generating event in history.

The physics provides no easy solution. You can’t sweep orbit clean — the debris is distributed across thousands of cubic kilometres, moving at different velocities in different directions. Active debris removal — using robotic spacecraft to capture and deorbit large objects — is being developed but is expensive and slow. The most practical approach, for now, is prevention: designing satellites that can be deorbited at end of life, either by reserved fuel or drag sails that accelerate atmospheric re-entry.

What Orbits Teach Us About the Universe

I find orbits endlessly fascinating because they’re one of those rare topics where extremely simple physics produces extremely rich behaviour.

The inputs are minimal: gravity (one equation), Newton’s laws of motion (three equations), and initial conditions (position and velocity at one moment). That’s it. From these ingredients, you get circular orbits and elliptical orbits, escape trajectories and capture spirals, resonances and Trojan points, orbital precession and tidal locking, Hohmann transfers and gravity assists.

Every planet, every moon, every asteroid, every binary star, every galaxy in a cluster, every satellite and every piece of space junk — all following the same physics. The same equation that governs a GPS satellite governs the orbit of a star around the supermassive black hole at the centre of the Milky Way. Scale changes by a factor of 10¹⁵. The physics doesn’t budge.

Newton’s cannonball thought experiment is over 300 years old, and it still captures the essence perfectly. An orbit is just falling and missing. Falling toward something you never reach, carried sideways by momentum that gravity can curve but never kill.

There’s an elegance in that — a thing perpetually drawn toward another, perpetually arriving, never quite there. Physics textbooks don’t usually dwell on the poetry of it, but I think they should. The mathematics is precise and practical. The image is genuinely beautiful.

The Moon is falling toward Earth. It has been falling for 4.5 billion years. And it will keep falling, keep missing, keep circling — long after every human who ever looked up at it is gone.