Orbital Mechanics
Apply Newton's laws to explain orbital motion: why orbit is continuously falling sideways rather than floating; how a gravity assist (slingshot manoeuvre) transfers momentum from a planet to a spacecraft; and why rockets need to reach a specific speed to enter orbit, with a conceptual (not algebraic) treatment of the Tsiolkovsky rocket equation
What a learner can do afterwards
- Explains that orbit is a state of continuous freefall: the spacecraft is falling towards Earth but moving so fast horizontally that it keeps missing
- Describes how a gravity assist works: a spacecraft flying past a planet gains speed by 'borrowing' from the planet's orbital momentum
- Explains the key insight of the rocket equation: the ratio of fuel to final spacecraft mass grows exponentially with required Δv, explaining why large rockets are mostly fuel
1 · Read
You already know gravity pulls every object toward every other object, and that near Earth this pull yanks things straight down. A satellite in orbit feels that same pull. So why does it stay up instead of crashing? It doesn't stay up. It's constantly falling toward Earth. It just moves sideways so fast that as it falls, the ground curves away underneath it, and it keeps missing.
The International Space Station orbits about 400 kilometers above Earth, close enough that astronauts would fall if gravity stopped. But the ISS also moves sideways at about 7.7 kilometers every second. In the time it falls a little toward Earth, Earth's surface has already curved away by that same amount, so it never gets any closer. Astronauts aren't away from gravity. They're in constant freefall together with their ship.
Picture tossing a ball straight at an oncoming train so it bounces off the front. The ball comes back faster than you threw it, because it picked up some of the train's motion. A spacecraft flying past a moving planet does something similar, with gravity instead of a bounce. As it swings by, it borrows a tiny bit of the planet's momentum and leaves faster than it arrived. The planet slows down too, but it's so much heavier that the change is too small to ever notice.
An orbit is a continuous fall that keeps missing the ground, a gravity assist borrows speed from a passing planet, and rockets carry so much fuel because each bit of extra speed costs even more.
More to read
3.5 Motions of Satellites and Spacecraft
An orbit is a state of continuous freefall. A spacecraft in orbit is falling toward Earth but moving so fast horizontally that it keeps missing the ground. The International Space Station orbits at about 400 km altitude, where gravity is still about 90% as strong as on the surface. The astronauts float not because there's no gravity, but because they and the station are falling together. To reach orbit, a rocket must accelerate to about 7.8 km/s sideways. This requires enormous amounts of fuel. The Tsiolkovsky rocket equation shows that the fuel-to-payload ratio grows exponentially with the required velocity change, which is why rockets are mostly fuel tanks.
3.5 Motions of Satellites and Spacecraft
A gravity assist (slingshot maneuver) lets a spacecraft gain speed by borrowing momentum from a planet. As the spacecraft flies past a planet, the planet's gravity pulls it along, adding to its velocity relative to the Sun. The planet loses a tiny, imperceptible amount of orbital momentum. This technique has been used by Voyager, Cassini, and many other missions to reach the outer solar system without impossibly large rockets. Newton's laws explain why this works: the interaction is an elastic gravitational collision where momentum and energy are conserved.
Kepler's Laws of Orbital Motion
Kepler's laws describe how objects move under gravity. The first law says orbits are ellipses with the central body at one focus. The second law says a line from the planet to the Sun sweeps equal areas in equal times, meaning planets move faster when closer to the Sun. The third law relates orbital period to distance: the square of the period is proportional to the cube of the semi-major axis. These laws apply to planets, moons, and spacecraft alike. Newton later showed they derive from his law of universal gravitation.
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8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.