![]() ![]() not at the ground) will fly away and never return (see orbit E in the Newton’s Cannonball diagram.) These are known as hyperbolic 3 orbits. ![]() However, an object with a high enough speed in the right direction (i.e. Periodic comets like Halley’s comet follow elliptical orbits too, but very eccentric (i.e. The orbits of all the planets in the Solar System are elliptical 2. What if we fired the cannonball slightly faster than required for a circular orbit? Then, it would enter into an elliptical orbit around the Earth, as shown in orbit D of the Newton’s Cannonball diagram. Why astronauts seem to be weightless in space (image by author, CC BY 4.0.) They seem weightless because the ISS is falling at exactly the same rate that their bodies are. A more accurate (and perhaps pedantic) term is ‘freefall’. Hence, it is a misnomer to say that astronauts floating on the International Space Station are ‘weightless’ or in ‘zero gravity’ because they are still under the influence of the Earth’s gravity – at the ISS’s altitude, the force of gravity is about 90% as strong as it is at sea level. A spacecraft in a low circular orbit, for example, would need to travel faster than one in a high orbit, because a planet’s gravity is stronger the closer you get to it. The speed of a spacecraft in its orbit depends on the orbit’s shape, the planet’s mass, and its current distance from the planet’s center. In low Earth orbit, a spacecraft would need to orbit at about 7-8 km/s to achieve this. In other words, it’s travelling fast enough that the ground curves away under the spacecraft as it ‘falls’ around the Earth, but not so fast that it flies off into space forever. In a circular orbit, centrifugal force 1 balances the force of gravity. In the present day, this is essentially how spacecraft stay in orbit. But fire the cannonball fast enough, and it will travel so far that it will follow a complete circle and hit you in the back of the head (as shown in orbit C of this diagram): Newton’s cannonball thought experiment, as described in Principia (image source: Wikimedia Commons.) If one fires a cannonball from this cannon, it will travel horizontally until the Earth’s gravity pulls it back to the ground. ![]() In it, he asks us to imagine a cannon on top of a very tall mountain – so tall that its peak is in space. His work Principia, often considered one of the most important works in the history of science, proposed a clever thought experiment. Orbits were famously described by Isaac Newton in 1687 (get used to seeing his name a lot).
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