Relative Observed Speed: Earth-Falling Objects & Time Dilation

[LM542]

When an object is flying to the Earth and it's increasing it's speed through gravity, does a remote observer see this increase of speed too, or will he see the object moving at a constant speed?

And another question:
Is there any time dilation by the remains of an object that hits a planet (that is not spinning), compared to an object that's flying in the same orbit as the planet. The first object has lost it's momentum and is now moving with the same speed as the second object. Is the time dilation on both objects the same?

 

[PeterDonis]

When an object is flying to the Earth and it's increasing it's speed through gravity, does a remote observer see this increase of speed too

By "speed" I assume you mean "speed relative to the Earth". Speed is relative, so you have to specify what it is relative to.

Assuming that's what you meant, then yes, a remote observer, assuming he was able to see the object in the first place (and the Earth, for that matter), would see the object's speed relative to the Earth increasing.

Is there any time dilation by the remains of an object that hits a planet (that is not spinning), compared to an object that's flying in the same orbit as the planet.

It depends on the planet and the trajectories the two objects are following. In general, yes, an object's elapsed time in a curved spacetime depends on the path the object takes through spacetime.

Is the time dilation on both objects the same?

Time dilation in a gravitational field doesn't just depend on speed. It also depends on altitude. You haven't given enough information to compare the time dilation of the two objects.

 

[LM542]

@PeterDonis:
1. Doesn't the time slows down for the object?
The closer the object comes to the Earth the slower it's time goes, so shouldn't the remote observer see a constant motion?

2. Does gravity even have a time dilation effect on matter that's not giving into gravity? The time of an object that's flying to the Earth (right before it reaches the ground) is slower than an object that's lying on the ground, but when it's hitting the ground it, it will be the same.

 

[PeterDonis]

Doesn't the time slows down for the object?

Not according to the object. According to the remote observer, yes, the object's time will appear to go slower, but that's a separate thing from the speed the remote observer measures for the object.

It is true that, if the central mass is not the Earth but a black hole, the object's motion will appear to the remote observer to slow down when it gets close to the hole's horizon. (The Earth is nowhere near compact enough for its mass for any effect like this to show up.) But up until that point, the object will appear to the remote observer to be speeding up.

Does gravity even have a time dilation effect on matter that's not giving into gravity?

Yes. In a static gravitational field like that of the Earth, gravitational time dilation is a function of altitude--a clock at a lower altitude runs slower. There is also kinematic time dilation, which is a function of speed--a clock moving faster relative to the Earth runs slower.