[simplified (OP)]

Can gravitational slowing of time be in neutral gravitational field? For example in center of a mass?

[JP]

Yes.  A clock placed at the center of the earth will run slower than a clock far out in space.  This is because even though the gravitational force cancels out at the center of the earth, there is still a lot of gravitational field there, which can dilate time.

[imatfaal]

Remember that the slowing of time is due to differential gravitational potential - not the apparent force / field

[simplified (OP)]

Yes.  A clock placed at the center of the earth will run slower than a clock far out in space.  This is because even though the gravitational force cancels out at the center of the earth, there is still a lot of gravitational field there, which can dilate time.

Thank you.Is that proved by any experiment?Or only theoretically?

[JP]

Good question, simplified.  As far as I know, no one has done that exact test, which would be difficult--you'd have to go to the exact center of a massive spherical object.  However, time dilation has been very well tested at various heights above the earth's surface and has been found to agree very well with general relativity's predictions.  GR has also been very well tested in a lot of other cases.  It would be quite odd if it worked so well in every case except a clock at the earth's center. 

[simplified (OP)]

Good question, simplified.  As far as I know, no one has done that exact test, which would be difficult--you'd have to go to the exact center of a massive spherical object.  However, time dilation has been very well tested at various heights above the earth's surface and has been found to agree very well with general relativity's predictions.  GR has also been very well tested in a lot of other cases.  It would be quite odd if it worked so well in every case except a clock at the earth's center. 

Let's consider mental experiment: we do an approach of any star to the Sun(in flatness of Earth's circulation around the Sun), does it increase  period of Earth's circulation around the Sun? Please answer only by Newton's physics without relativity.

[MikeS]

Remember that the slowing of time is due to differential gravitational potential - not the apparent force / field

If you imagine the different degrees of time dilation around a spherical object as being 'time shells' then each shell represents a gravitation potential and particular time dilation.  Each one is discreet but relative to the others.

[simplified (OP)]

Remember that the slowing of time is due to differential gravitational potential - not the apparent force / field

If you imagine the different degrees of time dilation around a spherical object as being 'time shells' then each shell represents a gravitation potential and particular time dilation.  Each one is discreet but relative to the others.

'Time shells' remind about the sky of ancient Greeks. []

[JP]

Good question, simplified.  As far as I know, no one has done that exact test, which would be difficult--you'd have to go to the exact center of a massive spherical object.  However, time dilation has been very well tested at various heights above the earth's surface and has been found to agree very well with general relativity's predictions.  GR has also been very well tested in a lot of other cases.  It would be quite odd if it worked so well in every case except a clock at the earth's center. 

Let's consider mental experiment: we do an approach of any star to the Sun(in flatness of Earth's circulation around the Sun), does it increase  period of Earth's circulation around the Sun? Please answer only by Newton's physics without relativity.

Are you asking what happens if the earth's period of rotation if it were in an orbit closer to the sun?  It would decrease, from Kepler's third law.  This can also be seen by looking at Mercury, which only takes 88 days to go around the sun.

[simplified (OP)]

Good question, simplified.  As far as I know, no one has done that exact test, which would be difficult--you'd have to go to the exact center of a massive spherical object.  However, time dilation has been very well tested at various heights above the earth's surface and has been found to agree very well with general relativity's predictions.  GR has also been very well tested in a lot of other cases.  It would be quite odd if it worked so well in every case except a clock at the earth's center. 

Let's consider mental experiment: we do an approach of any star to the Sun(in flatness of Earth's circulation around the Sun), does it increase  period of Earth's circulation around the Sun? Please answer only by Newton's physics without relativity.

Are you asking what happens if the earth's period of rotation if it were in an orbit closer to the sun?  It would decrease, from Kepler's third law.  This can also be seen by looking at Mercury, which only takes 88 days to go around the sun.

If second Sun will be on distance=1,ooo,ooo,ooo km to our Sun.Will it increase Earth's period of rotation around our Sun?

[JP]

Good question, simplified.  As far as I know, no one has done that exact test, which would be difficult--you'd have to go to the exact center of a massive spherical object.  However, time dilation has been very well tested at various heights above the earth's surface and has been found to agree very well with general relativity's predictions.  GR has also been very well tested in a lot of other cases.  It would be quite odd if it worked so well in every case except a clock at the earth's center. 

Let's consider mental experiment: we do an approach of any star to the Sun(in flatness of Earth's circulation around the Sun), does it increase  period of Earth's circulation around the Sun? Please answer only by Newton's physics without relativity.

Are you asking what happens if the earth's period of rotation if it were in an orbit closer to the sun?  It would decrease, from Kepler's third law.  This can also be seen by looking at Mercury, which only takes 88 days to go around the sun.

If second Sun will be on distance=1,ooo,ooo,ooo km to our Sun.Will it increase Earth's period of rotation around our Sun?

I'm not sure.  The speed a planet moves around the sun depends on the force the sun exerts on it, and it relies on the fact that the sun is always pulling it in towards itself.  If you put Sun 2 out in space, it would sometimes pull the earth towards the sun, and sometimes pull it away from the sun.  My guess it that it would leave it more or less unaffected, but you'd probably have to work out the actual math to figure it out for sure.

[imatfaal]

If second Sun will be on distance=1,ooo,ooo,ooo km to our Sun.Will it increase Earth's period of rotation around our Sun?

I'm not sure.  The speed a planet moves around the sun depends on the force the sun exerts on it, and it relies on the fact that the sun is always pulling it in towards itself.  If you put Sun 2 out in space, it would sometimes pull the earth towards the sun, and sometimes pull it away from the sun.  My guess it that it would leave it more or less unaffected, but you'd probably have to work out the actual math to figure it out for sure.

I reckon our orbit would be quite badly perturbed - at 10^12m the gravity of Sol_2 would be about 2% of Sol_1, and I reckon that's enough to make a nasty three body problem.  Of course as soon as our orbit is pulled out of whack we are no longer in equilibrium with jupiter etc as well.  It would be a fun ride - but I will pass