You Have Never Once Stood Still
Sit perfectly still and you are still moving hundreds of kilometers every second. The trick is that the motion only makes sense when you change the speed of time.
Start with how big it is
Earth is about 12,700 km across. The Moon sits about 30 Earths away. The Sun is 109 Earths wide, and its light takes about eight minutes to reach you. Past the planets is a thin cloud of icy comets, then the nearest stars, 4.37 light-years out. The Milky Way is about 100,000 light-years across. It is one galaxy among a neighborhood of galaxies, which sits inside a supercluster called Laniakea, which sits inside an observable universe roughly 93 billion light-years across.
That last number is only how far light has had time to reach us. It is the edge of what we can see, not the edge of everything.
The corkscrew
Earth circles the Sun at about 30 km per second. The Sun is not parked either. It circles the center of the galaxy at about 230 km per second and carries every planet with it. Put those together and Earth's real path is a long, stretched spiral, with the Moon looping around it the whole way.
The planets don't trail behind the Sun like a comet tail. They orbit it in a tilted plane while the whole system moves. And the spiral is far more stretched out than most videos show: in one year the Sun travels about 7 billion km, while Earth's orbit is only about 300 million km across.
Time is where the pattern hides
Watch a jogger in extreme slow motion and the movement looks strange, almost meaningless. Speed the footage up and you understand it instantly. The universe works the same way. At human speed, nothing seems to happen. Run it at hundreds of millions of years per second and you watch gravity pull matter into a glowing web of threads and knots, galaxies gather along them, and the space between groups of galaxies keep stretching.
Whether the universe as a whole also swirls is an open question. A few recent surveys hinted that galaxies spin one way more often than the other, but that is debated and unconfirmed. The app has a what-if switch so you can see the idea, clearly marked as a what-if.
The time traveler's problem
Most time-travel stories only change the date. But if you jump back one year and stay at the same spot in space, Earth isn't there anymore. Hold still against the galaxy and you would land about 7 billion km from home, in empty space.
It gets harder. There is no single "still" place in space, so the answer depends on what your machine holds still against: the Sun, the galaxy, or the leftover glow of the Big Bang. Earth also moves 230 km every second, so to land within a meter of the ground your timing has to be right to about four millionths of a second. Even then, Earth would hit you at full speed unless you also matched its velocity. Get it slightly wrong and you arrive three feet underground, or high in the air.
Aiming at empty space
Rockets have the same problem, minus the time machine. You can't aim a Mars rocket at Mars, because Mars moves while you fly. You aim at the empty spot where Mars will be on arrival day, months later. That is why good launch windows only open about every 26 months, when Earth and Mars line up so the trip costs the least fuel.
Back to the apple
Around 1666, an apple fell in an orchard in Lincolnshire, England, and Isaac Newton wondered why it fell straight down. Since then Earth has gone around the Sun more than 360 times. Seasons have turned the tree from blossom to bare branch hundreds of times, and the Sun has carried all of it billions of kilometers through the galaxy. The tree never noticed.
What we know, and what we're guessing
The sizes, speeds and planet positions here come from real measurements, rounded so they're easy to hold in your head. The ideas at the edges are different. Maybe our universe is one square in a much bigger grid. Maybe time runs at different rates on different levels of existence. Those are questions, not findings. They are worth asking anyway, because nobody ever found anything by assuming they had already seen it all.