2 clocks: 1 on Earth, 1 on Mercury

[Leovinus]

Assume two identical clocks, one on Mercury, one on Earth, both initially set to the same time. Since Mercury is closer to the Sun and moving much faster than the Earth, I assume it's clock will run slower than Earth's clock. After 1 Earth year, what will be the difference between the two clocks? <div class="Discussion_UserSignature"> </div>

 

[yevaud]

Hmmm. Not certain. That's one of those frame-dragging questions, and they're a real bear to work with.<br /><br />At a guess, possibly 1 second or so? <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[Leovinus]

That's not very interesting. <div class="Discussion_UserSignature"> </div>

 

[yevaud]

As these things go, it's not a huge gravity well, so frame dragging is present, but it's not a major factor. <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[yevaud]

http://www.nasa.gov/centers/marshall/news/news/releases/2005/05-066.html <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[Slate]

Not much but the important thing is there will be one, I think I recall reading that gravity also has influence on time. I wonder if the difference in mass between earth and mercury wood off set the difference in velocity and or would mercury’s closer proximity to the sun make a difference between the two clocks as well. <br />Good question Leovinus <img src="/images/icons/smile.gif" /> <br /><br />

 

[silylene old]

It depends whether gravity is assumed to pull or to 'push' ! <img src="/images/icons/wink.gif" /> <div class="Discussion_UserSignature"> <div class="Discussion_UserSignature" align="center"><em><font color="#0000ff">- - - - - - - - - - - - - - - - - - - - - -</font></em> </div><div class="Discussion_UserSignature" align="center"><font color="#0000ff"><em>I really, really, really miss the "first unread post" function.</em></font> </div> </div>

 

[farmerman]

Assuming that that the theory is true between Earth and Mercury would the same theory hold true between Earth and Mars? I believe that Spirit and Oppy. have internal clocks. Are there clocks slowly Changing? I don't know the speed of Mars compared to Earth, maybe they are close enough in speed where it doesn't matter.

 

[tony873004]

It's an interesting question. No GR experts out there?<br /><br />I doubt the Mars rovers have clocks accuate enough for such an experiment.<br /><br />I wonder what the difference would be for a clock on the equator vs. one at the north or south pole (Earth).

 

[vogon13]

I am assuming Messenger has a fairly accurate oscillator at least for the radio system and hopefully an accurate clock for the on-board electronics.<br /><br />So hopefully, when it gets there, we can have some real data to compare to the calculations.<br /><br /> <div class="Discussion_UserSignature"> <p><font color="#ff0000"><strong>TPTB went to Dallas and all I got was Plucked !!</strong></font></p><p><font color="#339966"><strong>So many people, so few recipes !!</strong></font></p><p><font color="#0000ff"><strong>Let's clean up this stinkhole !!</strong></font> </p> </div>

 

[yevaud]

This experiment was already conducted, years ago, by comparing an ultra-precise timepiece on the ground, and one on a jet travelling at altitude. And they did find exactly the time differential that was predicted. <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[Leovinus]

I'm not asking about a jet around Earth. I'm not even doubting that there will be a clock difference. I'm asking what the difference will be between Earth and Mercury. <div class="Discussion_UserSignature"> </div>

 

[mooware]

I'm wondering also if there would be a significant time dilation between Mercury and the sun?<br /><br />

 

[yevaud]

I've been doing some calculations as to this, and it's a very tiny amount of time.<br /><br />General relativity predicts an additional 43 seconds of arc due to frame dragging. This is in accordance with Einstein's predictions about GR.<br /><br />So that's an advance of 43 seconds of arc over a full century. It works out to a small fraction of a second per day. A very small fraction indeed, though it's altogether real.<br /><br />I know - boring. But that's the answer: I came up with 1.362 *10^-8 seconds difference. Which is to say, as we experience 1 second, an observer on Mercury will experience 1.00000001364 seconds.<br /><br />Hope that answers your question. And thanks. It forced me to recollect how to figure that out and actually crunch some numbers. <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[Leovinus]

I thought the faster moving clock would have time slowed down? <div class="Discussion_UserSignature"> </div>

 

[yevaud]

On the one hand, yes. But this isn't a case of moving faster. This is a special case where frame dragging due to proximity to the sun's gravity well slows the passage of time by a fractional amount.<br /><br />So, to an outside observer at relative rest, the clock on Mercury will run slower. <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[Leovinus]

Isn't that what I said? So I think that when the Mercury clock says 1 second, the Earth clock says more than one second.<br /><br />I hate relativity. <div class="Discussion_UserSignature"> </div>

 

[yevaud]

Ummm, you said it backwards. The observer on Mercury will experience the longer duration.<br /><br /><i>I hate relativity.</i><br /><br />Why does that remind me of the James T. Kirk line, "Gentlemen, Temporal Mechanics gives me a headache..."<br /><br /><img src="/images/icons/wink.gif" /> <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[Leovinus]

Since my Nuclear Physics class, I absolutely refuse to plug anything into Lorentz equations. <div class="Discussion_UserSignature"> </div>

 

[siarad]

I've been vexed by this forever.<br />These are atomic clocks which means atomic action is slower at the edge of the Universe due to it's speed but I read actions on Earth are the same throughout the Universe. <br />I seem to recall that the clocks on GPS satellites keep Earth time without correction, something to do with when they are set. Could be wrong so hope we have a GPS expert here.