How Planets Stay in Motion
When we look up at the night sky, the planets, moons, and stars all seem to move in predictable paths. But what keeps them in motion? Why don’t planets like Earth just fall into the Sun? The answer lies in orbital mechanics, a fascinating branch of physics that explains how celestial bodies move under the influence of gravity.
Newton’s Law of Universal Gravitation #
The first step in understanding orbits is gravity. Isaac Newton discovered that every object in the universe attracts every other object with a force proportional to their masses and inversely proportional to the square of the distance between them. Mathematically, this is written as:
$$ F = G\frac{m_1m_2}{r^2} $$
In this equation, \(F\) is the gravitational force, \(G\) is the gravitational constant, \(m_1\) and \(m_2\) are the masses of the two objects, \(r\) is the distance between their centers. This equation tells us that gravity gets weaker as objects move farther apart, but it never truly disappears.
Why Don’t Planets Fall Into the Sun? #
If gravity is always pulling planets toward the Sun, why don’t they just crash into it? The answer is inertia. Imagine throwing a ball forward—it moves in a straight line unless a force (like gravity or air resistance) acts on it. Now, imagine throwing the ball much faster. If it moves fast enough, it won’t hit the ground but will keep falling around the Earth, creating an orbit.
Planets work the same way. They are constantly “falling” toward the Sun due to gravity, but because they are also moving sideways at high speeds, they keep missing the Sun and continue in their orbits. This balance between gravitational pull and forward motion is what keeps planets in stable orbits.
Kepler’s Laws of Planetary Motion #
Before Newton, astronomer Johannes Kepler studied how planets move and discovered three important rules:
Elliptical Orbits: Planets don’t move in perfect circles but in ellipses, with the Sun at one of the two foci. This means that a planet’s distance from the Sun changes throughout its orbit.
Equal Areas in Equal Time: A planet moves faster when it is closer to the Sun and slower when it is farther away. This means that in any given time period, the planet will sweep out equal areas in space, even though it covers different distances.
The Orbital Period Rule: The farther a planet is from the Sun, the longer it takes to complete an orbit. Mathematically, this is written as:
$$ T^2 \propto a^3 $$
where \(T\) is the planet's orbital period and \(a\) is the semi-major axis (the average distance from the Sun).
These laws helped astronomers accurately predict planetary positions before the concept of gravity was even fully understood.
Orbital Speeds and Escape Velocity #
For an object to stay in orbit, it needs to travel at just the right speed. If it moves too slowly, it will spiral toward the massive body it’s orbiting. If it moves too fast, it will break free and fly off into space. The minimum speed needed to escape a planet’s gravity is called the escape velocity, given by:
$$ v_e = \sqrt{\frac{2GM}{r}} $$
Where \(M\) is the mass of the planet and \(r\) is the distance from its center. For Earth, this is about 11.2 km/s (25,000 mph)—the speed rockets must reach to leave Earth's gravity.
Spacecraft and Artificial Satellites #
Orbital mechanics isn’t just for planets—it’s crucial for spacecraft and satellites. Engineers must carefully calculate the right speed and altitude to place a satellite into a stable orbit. The International Space Station, for example, orbits Earth at about 7.66 km/s (17,100 mph), staying in motion due to the same physics that governs the planets.
Understanding these principles allows us to send probes to distant planets, land rovers on Mars, and even predict how celestial bodies will move far into the future.
Sami Elsayed is a Senior at TJHSST, and the current Lead Sysadmin at the tjCSL. He’s the Co-Founder of the Cardinal Development Organization, and the current Head Writer of “The Techbook.”