Chompers said:
Thanks for the reply. That's what I thought I read, but it raised a question for me: if gravity is warped space, then why does it take an acceleration of 11.2km per second to escape Earth's gravity? I'm clearly missing something here.
Escape velocity is defined as the minimum velocity an object needs to go from the surface of the object to "infinity". In other words, if you were to launch a rocket with a velocity exceeding 11.2km/s, it would never fall back to Earth. Ever.
In gravitational fields of low to moderate strengths, the equations of General Relativity generally reduce down to those of Newtonian Gravity. All the extra stuff that GR adds is negligible until you get into very strong fields. GR makes all the same predictions as Newtonian gravity and then adds many more on top of that. Those extra predictions are just not important in almost all situations involving spaceflight today. Who cares if the GR equations are accurate to 2 millimeters if you only need to be within a hundred kilometers (totally made up numbers, but I hope that gets my point across)?
Chompers said:
I may not be understanding and/or asking the question correctly. I was thinking about space as a trampoline (as many explanations use this as an analogy), and an object like the sun bending the trampoline/space around it. A second object like a spacecraft enters the curved space, and would then presumably require additional thrust to traverse that curved space and leave (ie head out into space). If gravity is the curvature of space, why would additional thrust be required to escape it? This is what propmpted my initial question of whether gravity is the curvature of space or curves space and attracts other objects.
The key here is that your spacecraft starts far away from the Sun, travels close to it, and then back out. It accelerates under gravity during the approach, gaining velocity, which is then lost as it leaves. The net effect is that the spacecraft ends up with the same speed as it had before, just with a different heading. The final speed may or may not be enough to reach escape velocity for the Sun, it all depends on the initial velocity of the spacecraft . No extra thrust is needed unless you want to influence the final heading of the spacecraft . For a spacecraft on Earth, the craft starts with zero velocity relative to the Earth and can't use gravity to accelerate. So it has to be accelerated by a rocket engine up to a high enough speed to leave.
Don't get confused about the curved space stuff. As long as we aren't near an extremely massive or dense object, all of the equations of General Relativity can be simplified greatly and we can say that the net effect is essentially identical to Newtonian Gravity. Unfortunately if you're trying to understand how curved space works, you're going to need to put in a significant amount of time and effort into learning Special Relativity and then moving on to General Relativity. And when I say that you need to put time and effort into learning these, I mean that you need to get into the math and work through example problems from textbooks. You can watch all the videos and read all the articles in the world, but until you put your nose to the grindstone you won't have anything but a passing familiarity with how GR works. It's a lot of hard work, but it can be very rewarding.
