# B Gravity and curved space

1. Jun 18, 2017

### Chompers

Hi all,

I'm doing some reading about special/general relativity, and have come across the ideas of curved space etc. I've very much a novice in physics, so please excuse my (possibly) stupid questions. For background, I'm interested in writing a sci-fi story, and would like to have at least some semblance of real science in it (although it's not a hard science story). At this stage it's just interesting questions rather than actual plot points.

So if gravity warps space, and the orbit of the earth around the sun is following a curved/geodesic path caused by the sun's gravity, is this warping of space/time gravity itself? Or is it just an effect of gravity on space/time? In other words, does gravity itself attract objects while also curving space, or just curve space?

Evan

2. Jun 18, 2017

### Staff: Mentor

Gravity doesn't warp space, gravity IS warped space. In other words, the effect we call gravity, the attraction that two bodies have on each other manifesting as a force in Newtonian gravity, is the direct result of mass and energy altering the geometry of spacetime.

3. Jun 18, 2017

### Chompers

Hi Drakkith,

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.

I may not be understanding and/or asking the question correctly. I was thinking about space as a trampoline (as many explainations 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.

Evan

4. Jun 18, 2017

### Staff: Mentor

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)?

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.

5. Jun 18, 2017

### Chompers

Many thanks

6. Jun 19, 2017

### A.T.

The time part is very relevant for what we interpret as "attraction":

7. Jun 28, 2017

### RTM

I like that post, A.T. I've seen the trampoline analogy, and have tried to visualize it in the 3-D world. So, at our real life distances, like dropping an apple from 5 ft, it's difficult to grasp space-time curvature. Are you saying that if you took a 5' apple drop, and ZOOOOOOOOMED in REALLLLLY closely, that it's similar to rolling the ball on the trampoline from 5' (exaggerated due to the zooming in) away from the big mass object that's bending the trampoline? Hope this makes sense enough to even ask.....

8. Jun 28, 2017

### A.T.

You cannot grasp space-time curvature from the trampoline analogy, because it's not an analogy for curved space-time, just space. There is no time axis on the trampoline.

In the apple animation above the time dimension is highly compressed, to make the weak distortion that the Earth causes visible. In natural scaling 1s corresponds to 1lightsecond.

9. Jun 28, 2017

### RTM

Ok, thanks, A.T. I think that I meant to say that I was trying to grasp curved space (not space-time...yet...). I want to try to understand curved space because earlier in this thread Drakkith said " Gravity doesn't warp space, gravity IS warped space." So I imagine that I will need to visualize/understand a 3-D total concept of the trampoline analogy. In my mind for that, I'm seeing a "bowling ball" not on a trampoline but suspended inside a huge block of say, light foam cushion material. And the "bowling ball" is actually a 360 degree vacuum sucking device, distorting the foam around it and pulling it inward. But then when I fire an imaginary BB gun into the foam, I don't see the BB following the distortion of the foam toward the ball. Or will it? Oh well....I know this is crazy and you have better use of your time.

10. Jun 28, 2017

### A.T.

No, it's space-time.

No, you need to forget the the trampoline analogy.

11. Jun 28, 2017

### RTM

Ok, thanks.

12. Jun 28, 2017

### Staff: Mentor

Space-time. My mistake.

13. Jul 1, 2017

Once, one told me that gravity is a warp in space but we does interpret it as a force and not a force that may be seen as a warp in space.

14. Jul 1, 2017

### David Lewis

Gravitational time dilation can throw your space clock out of synch with Earth time if there is enough difference in potential.

15. Jul 1, 2017

### phinds

It's to be expected since you haven't yet learned how to tell time but just take up space. You'll get there.

16. Jul 1, 2017

### phinds

ANY difference in potential changes the sync, it's just a matter of how precise you can measure it.

17. Jul 1, 2017

### Staff: Mentor

It's not my fault. My watch is in a gravity well.

Classical gravity, aka Newtonian gravity, is a called a force, but gravity in General Relativity is usually not called that, though the effects near Earth and other areas of low mass/energy end up being mostly identical. Objects get closer together over time.

18. Jul 1, 2017

### Staff: Mentor

Certainly. But for the vast majority of applications the small difference doesn't matter. Certain applications, such as the GPS satellite system, require extremely precise timing that require taking GR into account, but most applications don't.