Time Dilation Comparison: Mass vs Speed

[aditya23456]

Firstly does a typical massed object surely prone to both kind of time dilations in its lifetime??
Consider 2 cases..
Firstly a person on a heavily massed planet where his time dilation is due to mass of that planet and in other case same person moving at c/2 away from any significant massed object nearby(This means he's not prone to any kind of dilation due to massive gravity fields).In such case,what should be mass of the planet to equalize both kind of time dilations(is there any relation for equating both)?
Figuratively,Which time dilation is more superior taking practicality into consideration(such as moving at c/2 isn't plausible than thriving on a planet of earth-like massed planet) ? Is there any field of study my question goes in too? If yes, please name it..Thanks in advance..I hope i made sense :)

 

[holtto]

not sure what you mean by equalize.

however, GPS satellite engineers from the US Naval Observatory take into account both gravitational and velocity dependent time-dilation.

in this case, grav time-dilation is more significant

 

[mfb]

The (absolute) gravitational time dilation on a planet (relative to free space) has the same order of magnitude as the (relative) time dilation of an object moving with escape velocity (relative to some observer). For earth, this is ~11km/s. To get c/2, you need a neutron star.

 

[aditya23456]

The (absolute) gravitational time dilation on a planet (relative to free space) has the same order of magnitude as the (relative) time dilation of an object moving with escape velocity (relative to some observer). For earth, this is ~11km/s. To get c/2, you need a neutron star.

WOW..thats interesting..Is there any derivation for this..?Isn't it surprising to be so?Just wondering if this deepens my understanding about time..

 

[mfb]

It has an actual connection in GR:

$$t_{surface} = t_{space} \sqrt{1-\frac{2GM}{rc^2}}$$
$$t_{moving} = t_{observer}\sqrt{1-\frac{v^2}{c^2}}$$

In the non-relativistic limit, the escape velocity is given by
$$v_e=\sqrt{\frac{2GM}{r}}$$
Plug it in, and you get the same factor in both equations.

Might be different for v ~ c (=> neutron stars and black holes).