spacetime curvature?

Question

it is mentioned that because of the space time curavture, we experienced things like gravity, hence planets revolve around sun and the solar system revolve round the Milky Way... But why wont we fall in towards the Sun? I mean how is it that Earth's orbit is stable and not spiral in.

Answer 1

Space is measured in cubic meters that it the dimension of its volume. If we take the mass of the Universe and divide by its volume of formation per seconds we obtain an invariant of space per unit time.
What is called curvature of space is really the mathematheal curvature of The volume of the substance of space. I dont Believe that Einstein had any orgument about that.

The Einstein stress energy Tensor divided by the curvature of space Tensor ratio becomes proportional to Newton Universal gravity invariant.
So we can either calculate Gravity field in terms of Einstein space curvature or Newton mass curvature.

Concerning the motion of Earth's Orbit ,it can only spiral out rather than spiral in.The reason for this is because the curvature of the mass of the earth continually decreases.So it orbit radius increases accordingly.
The Earth experiences this because gravity Field maintains the its rotational energy equilibbrium.
Equilibrium is not a static condition its a dynamic one. So stability is accepted only within the narrow range of variation.

The Velocity of the earth's moving mass does have 3 components;ONe velocity component moves toward the Sun(falls towards the Sun)The other is a tangential component moving at right angle to the radius vector and the sum of thes two components is the resultants motion of the earth.
The reason that the sun and the earth dont come to collide is because the sun is also revolving around with the earth at the same angular velocity.

Answer 2

Looks like you've already got most of the picture. As far as Earth staying in orbit around the sun, remember that even though the sun's gravity is constantly trying to pull Earth into it, Earth at the same time has enough velocity that's trying to hurl it outward into space. The two forces almost exactly cancel each other so the result is a stable orbit. This is the same principle behind why artificial satellites stay in orbit as long as they have enough linear velocity to offset the pull of Earth's gravity.

Answer 3

Attach a ball to a string and spin it around in a circle. It stays in the circle, doesn't it? What happens if you cut the string while it's spinning? The ball flies away in a straight line tangent to where it left the circle.

This is similar to the earth orbiting the sun. Newton's 1st law of motion states that objects in motion will remain in motion unless acted on by an outside force. The earth wants to move in a straight line, but it is being held in circular motion by the sun's gravity, called the centripetal force.

If the earth were to suddenly stop moving, yes, it would go towards the sun. But since the earth is moving, the centripetal force simply makes it continue along the same circular path.

Answer 4

Think about a marble rolling around the edge of a bowl. Eventually, it falls into the center, because it can't maintain it's constant velocity around the bowl - it loses momentum due to friction. But if it could maintain a constant velocity, it would stay in that orbit around the bowl forever. That's like the Earth in the Sun's gravitational potential well - but the Earth CAN maintain a constant velocity, because it's not losing energy to friction. If the Earth suddenly stopped in it's orbit, it WOULD fall into the Sun - fortunately, it's been going strong for billions of years.

Answer 5

The model of Einstein's space-time curvature works accurately, but is only a model. It is becoming outdated. Here's how it works, however.

Although gravity is a force "pulling toward" an object (not really, by the way, but for the example it is accurate), it can't stop the force that it is acting perpendicular (90 degrees) to. (Again, not really, but read on.)

If you take a ball on a string and spin it around, you pulling on the string is "gravity". If you release the string, the ball flys straight out of "orbit". So that force (the momentum) to go straight away was always there, it was just pulled toward you enough to curve it, but not enough to pull it into you. However, pull harder on the string, and eventually you will find it's limit, and collapse the "orbit".

Answer 6

Because the Earth has enough kinetic energy to compensate for the potential energy required to remain in orbit at this distance. It would have to lose this energy to spiral in, and nothing is there to slow it down.

Answer 7

because the core in the earth is a big rotating ball of liquid iron, which gives off enough friction to produce the atmosphere, and the earths magnetic fields which prevents the whole spririlng in from hapening