Why don't spacecraft get left behind once in deep space?

On earth, I know that if I throw a tennis ball straight up while in a car, it comes straight back down thanks to Newton's first law. The ball, the air in the car, and myself are all moving at a speed, and when I throw the ball up, I'm actually throwing it forward relative to someone standing on the street.

What I don't understand is that once I leave the atmosphere of earth and reach the vacuum of deep space, where the earth's gravity is no longer keeping me in orbit (right?), why do I not behave like a tennis ball that was thrown too high in a convertible? Is it really that simple that I'm continuing along within the solar system as it orbits the galaxy center simply because I was already going the same speed? Is the barycenter of the solar system dragging me along through the galaxy?

Unfortunately I'm ignorant as to what effect I should Google to understand how, if I turn off rockets and coast, I'm coasting at enough speed to keep up with the solar system. Please someone help me.

• A common misconception about space is that gravity 'turns off' once you're out of the atmosphere. Earth's gravity in fact extends infinitely far and slowly decreases. If you fire a rocket hard enough straight upwards, it will go out of the atmosphere into space, then come back down through the atmosphere to earth. Orbit is achieved by going very fast horizontally, so that you are constantly 'missing' the ground as you are falling towards it. In reply to your title question, spacecraft are left behind all the time. This XKCD gives a good explanation of all this: what-if.xkcd.com/58 – Ingolifs Dec 3 '19 at 23:23
• I understand that gravity and technically all forces are infinite, but what I don’t get is once I’ve exited the orbit of the earth and go careening off on my centrifugal path not stuck to any planetary body’s orbit, if I happen to careen “down” relative to the planets’ orbital plane, would the solar system leave me behind? Or would I continue to keep up with the solar system due to some combination of inertia and gravitational pull from the sun? – Michael Guinn Dec 4 '19 at 0:20
• Ah I see. Once you've reached the escape velocity of earth (or whatever other planet), you enter orbit directly around the sun. You then have to fire your rocket a lot more to get fast enough to escape the solar system. – Ingolifs Dec 4 '19 at 0:34
• To understand the amount of energy required to achieve escape velocity from the solar system, consider that the only objects we've made that have done so got MASSIVE delta-v boots from gravity assists. – Skoddie Dec 4 '19 at 19:05
• There are sounding rockets that go that go into space, even higher than the space station. But they go up and then come back down because they're not going fast enough horizontally to stay in orbit. (Or escape.) A satellite goes literally thousands of miles per hour to stay in orbit. – Greg Dec 4 '19 at 20:04

TL;DR:

Is the barycenter of the solar system dragging me along through the galaxy?

Yep!

What I don't understand is that once I leave the atmosphere of earth and reach the vacuum of deep space, where the earth's gravity is no longer keeping me in orbit

(minor quibble: you're still in an orbit, just not a closed orbit. This will be a hyperbolic trajectory. Your motion through space will still be curved to some degree by Earth's gravity, just not enough to pull you back again)

As Ingolifs pointed out, once you've reach terrestrial escape velocity, you'll end up in a heliocentric orbit that's probably quite similar to the Earth's own orbit about the Sun (depending on how fast you're going, of course). The Sun's escape velocity is somewhat higher than Earth's, so you'll need to be going at least another 12.3km/s faster (which is solar escape velocity minus Earth's orbital velocity) in order to escape the Sun's gravititational pull and travel into interstellar space. And then you'll be orbiting the galactic centre. If you reach galactic escape velocity, you'll be presumably orbiting the barycentre of the Laniakea supercluster (which of course has its own escape velocity). Such is life with a force with effectively infinite range.

why do I not behave like a tennis ball that was thrown too high in a convertible?

On the assumption that you're not driving your convertible in a vacuum chamber (you'd be hard pressed to find one big enough... maybe the moon landing conspiracists can point you in the direction of one?) when you throw that ball up its forward velocity will initially match that of the car but drag will slow it down and so it will drift backwards with respect to the car. In space of course there's not really enough stuff to provide much drag under normal circumstances, so you'll just keep on travelling with the velocity you had when you were "thrown". If you escape Earth's sphere of influence, you'll initially enter into an Earthlike heliocentric orbit, because of the velocity you had before you escaped.

• Thanks! And just one more potentially obvious follow-up: would it then require less force to reach solar escape velocity if my direction is opposite the path of the sun around the Milky Way? You might say "down" relative to the plane the planets orbit, or "backward" relative to the plane that bodies orbit the Milky Way. – Michael Guinn Dec 5 '19 at 1:59
• @MichaelGuinn you could ask that as a separate question if you wanted details, but the best way to escape the galaxy is to point along the Sun's velocity vetor and accelerate that way, because then when you reach solar escape velocity you're already travelling at the sun's velocity relative to the galactic centre (about 200km/s), meaning you need less $\Delta_v$ to reach galactic escape velocity (about 550km/s). Accelerating in the opposite direction (retrograde) slows you down, dropping your orbit closer to the galactic centre. – Starfish Prime Dec 5 '19 at 8:43