https://www.syfy.com/syfywire/einsteins-hand-reaches-out-from-a-black-hole-and-torques-a-stars-orbit

Nick Mason is absolutely amazing in this clip. The whole movie is totally worth re-watching.

The problem is that NOTHING is stationary in space. If you took off from earth, you already share the earth’s orbital velocity about the sun, about 18 1/2 miles per second. If you aim at the sun and fire your rockets, you will simply add a small component of delta-vee at right angles to your path, which will only serve to slightly flatten your near-circular orbit around the sun into an ellipse–one that still goes nowhere close to hitting the sun.

In order to “fall into the sun” you’d have to flip your ship around and fire your rockets into your direction of travel, and come up with a delta-vee of 18 1/2 miles per second, an enormous energy expenditure. (Remember, the earth’s escape velocity is 7 miles per second.) This would then cancel out your forward progress entirely, and you’d fall straight into the sun! But you’d have to lift all the propellant you’d need for that maneuver off the earth’s surface in the first place. We just don’t have that kind of propulsion capability. In fact, even if you could miraculously put a fully fueled Saturn/Apollo multi-stage rocket into space, it still wouldn’t have the suds to send a payload into the sun.

Going down gravity wells from orbit takes exactly as much energy as it takes to climb out of them into orbit. If it wasn’t for atmospheric braking, we’d never be able to return to earth from LEO.

However, we ARE clever enough to exploit gravitational assists from other planets.

OH, and BTW, I remember distinctly, the first time I ever listened to the Floyd I told myself “This is the kind of music starship sailors will relax to when they’re off watch.” Thanks for the memories.

In my meager understanding of these things, it is not easy to fly straight into the sun. The curvature of spacetime makes that impossible? Unless the object has incredible momentum?

This holds for an object falling an enormous distance, where the gravitational force is considerably weaker at great distances from the planet (which is why you have to use calculus to integrate the force across the distance r).

For the special local case, say, dropping a cannonball off a tall building, the gravitational acceleration g at the top of the building is almost identical to that at ground level (roughly 10 m/s^2), there is no need to integrate. You can just use Mgh, where h is just the height of the building in meters. So when you drop a mass M Kg off the top of a building, its initial KE is zero, and its PE = Mgh. When it hits the ground, the KE = 1/2Mv^2 and the PE is 0.

The total PE of any object “at infinity” will be equal its KE when it finally hits the ground. The KE at that instant will be equal to the Object’s KE at escape velocity. In other words, the energy required to leave a gravity well is equal to the energy released when you fall into it.

For a more rigorous discussion, see

https://en.wikipedia.org/wiki/Escape_velocity

To move into a higher orbit, you have to add orbital velocity by accelerating in the direction of motion. To drop to a lower orbit you need to accelerate opposite the orbital motion. I.e., slowing down sends you sunward, speeding up sends you away from the sun. Either one requires an input of energy from an external source (either a rocket motor or another gravitational body).

Another way of thinking about it is that staying in any orbit requires a certain amount of energy. If you want to go down the gravity well you have to bleed some of it off. Of course, this only holds true of orbiting bodies. If you were to miraculously place an object, stationary, anywhere in the gravity well, it would just fall in.

Everything in the solar system is in some kind of orbit around the sun. It is either an elliptical orbit, a parabolic orbit (its just passing through) or it already fell in a long time ago. Even a spacecraft which has exceeded earth escape velocity and is therefore no longer in orbit around Earth is still in orbit around the sun.