Relative Time: Earth vs Mars - A Physics Enthusiast's Question

[Wh17e]

Hi, everyone.

I'm new here so I'll introduce myself: I'm not a physicist, just a physics enthusiast. Although I have studied some physics at school and college, I've never been taught relativity, which I've kind of learned about on my own.

My question might seem stupid to you, and I apologise if it is, but I've been thinking about this for some time now, and I can't get to the bottom of it. Here's the thing:
The Earth moves at its own orbital speed around the Sun, and so do the other planets in this system. But as they have different distances to the sun, they travel at different speeds. Those speeds relative to the speed at which Earth is moving, I reckon they are pretty big.
So, if we ever were to send people to Mars, would their time grow further and further apart from ours every year?

I apologise in advance for the weird English (I'm not native), and thanks for any answers you might give me.

 

[Orodruin]

A priori, there is a time dilation effect due to the moving of the planets as well as due to the gravitational time dilation. However, the velocities are actually pretty small compared to the speed of light so the effect is very small. The orbit velocity of Mercury (which is the fastest) is about 0.0001c.

 

[HallsofIvy]

Very, very slightly, yes. But the difference would be overshadowed by the complications of communicating over such a distance and the time differences caused by speeds going to and from Mars, anyway. The difference would probably be un-noticeable.

 

[wabbit]

A priori, there is a time dilation effect due to the moving of the planets as well as due to the gravitational time dilation. However, the velocities are actually pretty small compared to the speed of light so the effect is very small. The orbit velocity of Mercury (which is the fastest) is about 0.0001c.

... and relativistic corrections go as $\sqrt(1-v^2/c^2)$, which for $v=0.0001c$ yields a correction of 0.0000005%.

 

[Dale]

That amount of time dilation is definitely measurable with modern precise clocks, but not noticeable on a "human" scale. I.e. you couldn't use time dilation to pretend that you remembered your brother's birthday and claim that it is just relativity's fault.

 

[wabbit]

you couldn't use time dilation to pretend that you remembered your brother's birthday and claim that it is just relativity's fault.

What? Now I'm in trouble!

Otherwise, with precision clocks if I'm not mistaken GPS sattelites do take into account time dilation, both from speed and gravitational - there might be a thread about this somewhere in the forum. Not sure what their velocity is, though.

 

[PeroK]

Hi, everyone.
Those speeds relative to the speed at which Earth is moving, I reckon they are pretty big.
So, if we ever were to send people to Mars, would their time grow further and further apart from ours every year?

A very rough calculation. For something traveling at 10,000 m/s relative to Earth, the time dilation would be about 1.5s per century.

 

[Dale]

What? Now I'm in trouble!

Otherwise, with precision clocks if I'm not mistaken GPS sattelites do take into account time dilation, both from speed and gravitational - there might be a thread about this somewhere in the forum. Not sure what their velocity is, though.

Yes it is noticeable with precision clocks. No it is not noticible with birthday cards.