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Inertia describes how objects that are moving will stay moving, and objects that are not moving will stay not moving, unless something makes their speed or direction change. That's the layman's way of saying it. It's classical physics, Isaac Newton's stuff, specifically his first law of motion.

If we're talking about the movement of spaceships, it means this; if an engine fires and generates thrust, that's the engine exerting force on a not-moving spaceship. Once the spaceship starts moving, the engine can shut off, and the ship will stay moving. That's because in space there's nothing to slow or stop it.

In the atmosphere of a planet, air resistance will slow or stop the ship, so it will need to keep its engines going. On the surface of water or the ground, the friction of the ship's interaction with said surface will slow or stop the ship, even if it's on a planet with no air.

In space, there's no air resistance or friction. The ship will keep going forever. In fact, if you don't turn off the engines, it will go faster and faster until it approaches the speed of light and all kinds of physics wonkery will start to happen. That's (one reason) why spaceships shouldn't keep accelerating, rather they should fire engines in short bursts to gain speed, then preserve fuel while “coasting” at a constant velocity. Likewise, to decelerate, the ship will need to have engine exhaust ports—“thrusters”—on the front section, or the ship will need to perform a turnaround maneuver and fire engines again to slow or stop (my preferred method of slowing or stopping spaceships in my own books).

All of this is because of inertia. When writing about space, not only do you have to remember that there's no gravity, you also have to remember that there's no force to act on bodies at rest or in motion. Well, no blind or uncontrolled force.

It's not just spaceships. This applies to spacemen and spacewomen, space dogs and space cats, space rocks and space teapots, etc.

Consider this scenario; a ship is accelerating at one gravity (9.806 m/s2, or about a 35 kph increase every second, amounting to a speed of 126,000 kph or about 78,000 mph after an hour of accelerating). By accelerating at this rate for only one hour, a ship can travel 3,024,000 km or about 1,880,000 miles in one full day.

“One gravity” means exactly what it sounds like. That's the rate of acceleration that creates a sense of gravitational force equivalent to standing on the surface of the Earth. “1g.” In the hour the ship is accelerating, there's gravity on the ship. This is from the thrust of the engines pushing the ship against anything or anyone inside. So, if someone is standing on the deck, and the engine thrust is beneath their feet, they feel gravity like Earth, or less, or more, depending on how many g of acceleration is being produced.

Once the acceleration stops, the person would fly toward the ceiling above their head. Likewise, if the person is weightless because the ship is not accelerating (different from not moving), when the ship starts accelerating, the person would sink to the deck, because the engines would be pushing the deck up to them. All of this is due to inertia.

It works in other ways too. A weightless crewman pushes his/herself off a wall to float across a room, that crewman will need to stop themselves by grabbing something, or they'll smack into the far wall.

Here's a book you should consider reading; 2001: A Space Odyssey, by Arthur C. Clarke. Not only because it's an awesome book, but also because it describes things like microgravity, using the apparent centrifugal force to generate artificial gravity, and movement in space governed by inertia. After that, keep reading Clarke, because lots of his books are great for real science in Science Fiction.

Once you learn the ins and outs of movement in space, you can start to come up with ideas for scenes in your own book. You can write a Science Fiction book without considering any of this (Isaac Asimov's Foundation series is a good example), but I personally believe all Science Fiction authors should understand this most basic of scientific principles anyway (Asimov certainly did, despite not using it in that series).

Another great book you can read to see how a master writes realistic scenes in space using the principles of inertia; Heavy Time, by C.J Cherryh. Not only does she delve deep into the concepts of microgravity and movement of bodies in space, she also dives deep into the physical effects of weightlessness on human bodies (it's also a riveting story, in my opinion).

So, I recommend you read up on inertia. Incorporate the principle into your scenes, or don't, but know what it's all about either way. For realistic space travel, inertia is as fundamental as grapes are to wine.