Why don't objects in orbit fall into the center?

[bigyinlee]

hi ... I am just a normal fella but physics fascinates me , I've been interested in general relativity ... string theory ...quantum mechanics and astronomy for some time now . I've got my head around what theyre about mostly lol ...but there is something i don't get !...i was hopeing someone could give me a laymans answer so bere with me I am no genius : ) ...my question ... i understand general relativity and how gravity in space time works (i think)..my understanding is that gravity holds our planet in orbit around our sun almost like a bowl ..if you like ... a warp ... this makes sense to me but then I am puzzled...if we are orbiting in this dish what is keeping us from gradually orbiting into the center of the dish ...apologies if its basic ...thanx : )

 

[mathman]

The planets are moving fast enough so that it doesn't happen.

 

[Mark M]

No, that picture is not correct. Gravity is the curvature of spacetime, not space. You're always moving through spacetime - if you aren't moving through space, you're still moving through time. Also, you always want to take the shortest possible path through spacetime. This is natural - when you throw an object through space, it takes the shortest possible path between you and the destination. It doesn't whiz around through space. Also, you take the the straightest possible path through time - you will observe an observer's clock ticking slower if he is moving relative to you, but you'll never see someone moving at a constant velocity have their clock constantly changing rates. They take a specific 'velocity' through time, even if it's different than yours.

So, you always want to take the shortest possible path through spacetime. However, matter curves spacetime. Since the shortest possible path between two points on a curved surface is curved, these means objects in a gravitational field take curved paths through spacetime. This means an acceleration through space, and shorter amounts of time elapsed in a gravitational field.

So, no 'bowl' involved.

 

[bigyinlee]

thanx for the response : ) ...ok i think I am getting it ...no bowls lol ...ok how about looking at spacetime like the surface of a trampoline and in the middle is a heavy canonball representing our sun ...matter curvs spacetime i get that ...and i think i get what your saying about shortest routes through curves however if i threw a tennis ball onto the trampoline it would follow the curve in an 'orbit' ...but this orbit would decrease gradualy until and also get faster until it hits center ...now understanding gravity is pulling the ball down not to the center like our sun i still don't grasp what force is keeping us in perfect orbit or...is it ?? is our solar system expanding too..and its expansion stopping us from going down the plug hole as it were ?? : )

 

[Mark M]

thanx for the response : ) ...ok i think I am getting it ...no bowls lol ...ok how about looking at spacetime like the surface of a trampoline and in the middle is a heavy canonball representing our sun

See, but this is a problem - one direction must represent time. So, we must place a cannonball at every point on a line going across the trampoline, to represent the fact the Sun sticks around for longer than one moment.

Also, we must attach something to the object we're rolling across that propels it forwards - remember, objects must always move forward through time.

... i still don't grasp what force is keeping us in perfect orbit or...is it ?? is our solar system expanding too..and its expansion stopping us from going down the plug hole as it were ?? : )

So, you're question isn't unique to GR, but gravity in general. You're asking why, if gravity pulls us towards the Sun, how we can stay in orbit.

The answer is because the Earth has a very large velocity. If you tie a rope to a rocket and allow that rocket to take off, you won't be strong enough to hold it down. Similarly, gravity isn't strong enough to pull the planets into the Sun. However, if you were strong enough to hold onto the rope, the rocket wouldn't be able to continue to move away. However, he would continue to move. Since you're holding onto the rope, he will continue to go around you. This force is called centripetal acceleration, the inward force during circular motion.

Similarly, gravity is strong enough to prevent planets from escaping. However, it's not strong enough to pull them in. So, they maintain orbits around the Sun.

 

[bigyinlee]

thanku mark : ) that's brilliant I've really learned something there : )