Space-Time itself is inflating at an extreme rate so everything embedded in Space-Time is in motion just from that alone. Whether the bubble of Space-Time is also in motion within some super framework of other Universes is unknown and will probably forever remain unknown. What we observe is that the majority of observable Galaxies are all heading away from our Milky Way Galaxy, and as Edwin Hubble discovered the further away and farther back in time the observed Galaxy is the faster it is heading away from every other Galaxy. There are local groups of Galaxies orbiting around the Milky Way and the Andromeda Galaxy among others is heading directly towards a collision with the Milky Way Galaxy. So to answer the basic question everything is in motion. The Earth and Solar System are orbiting the Milky Way in excess of 600,000 miles per hour. The Earth orbits the Sun at about 60,000 miles per hour. The Milky Way Galaxy is traveling towards the Andromeda Galaxy at about 1 Million miles per hour. The local group of Galaxies is traveling within the Virgo Super Cluster of 100,000 Galaxies at about 50 million miles per hour. Note these are all just rough numbers and should be researched further but this is what I remember from an Astronomy lecturer at Kitt Peak Observatory, Arizona. Standing on the Earth which is 24,000 miles in circumference rotating once every 24 hours means that everything on the Earth's surface at the Equator is traveling at about 1,000 miles every hour. So calculate how many miles you are away from where the Earth and Solar system, Milky Way, Local Group was when you were born. Now imagine a time traveler that forgot that time is not entrained with the Earth and they successfully blip out of Time for 1 hour. Where will they reappear in 1 hour? Better have a Starship handy if they wish to return to the Earth.