# A question

#### aznpride2pac

There are 2 people, who are twins. One was born on earth, and the other was born in space. Because earth orbits the sun, so the twin born on earth is like traveling on earth. So, would the twin born on earth age slower than the twin who stayed at space?

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#### mathman

What is space born twin motion relative to earth? (How did they get born in different locations from the same mother???)

#### EnumaElish

Homework Helper
mathman said:
How did they get born in different locations from the same mother???
Excellent question.

aznpride2pac: see this and following posts.

#### shrumeo

how could they be twins if one was born in space and the other on earth?
o well, carry on.... :)

#### EnumaElish

Homework Helper
Are they "Irish twins"? If so, they may not agree on simultaneity.

#### yogi

I assume you mean that there is some point in space that the earth passes by each year in its orbit - and one twin remains fixed at that location and the other rides along with the earth. To answer the question, you will need to know how one twin acquired motion wrt to the other - did they both get plunked out on earth and then one got snagged on a sky hook as the earth traveded along in its orbit - or did they arrive in space and one then hitched a ride as the earth passed by. When you decide this, you can say that the twin that acquires motion after they were at rest in the same frame - will age slower.

#### pervect

Staff Emeritus
aznpride2pac said:
There are 2 people, who are twins. One was born on earth, and the other was born in space. Because earth orbits the sun, so the twin born on earth is like traveling on earth. So, would the twin born on earth age slower than the twin who stayed at space?
There is not enough information to give a direct answer for the problem as stated.

For instance, if we assume the second twin is hovering with a rocket or light sail, stationary with respect to the sun, way out in the Oort cloud, the space twin will age [correction- faster, dang it] than the Earth twin because of the difference in gravitational potential. While I have not performed an exact calculation for this case, I expect that the gravitational time dilation will outweigh the velocity-induced time dilation, much as it does for GPS satellites. In this case, the space-twin would be out of the gravity well of both the Earth and the Sun.

http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Unit5/gps.html [Broken]

To achieve this level of precision, the clock ticks from the GPS satellites must be known to an accuracy of 20-30 nanoseconds. However, because the satellites are constantly moving relative to observers on the Earth, effects predicted by the Special and General theories of Relativity must be taken into account to achieve the desired 20-30 nanosecond accuracy.

Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see their clocks ticking more slowly (see Lecture 32). Special Relativity predicts that the on-board atomic clocks on the satellites should fall behind clocks on the ground by about 7 microseconds per day because of the slower ticking rate due to the time dilation effect of their relative motion.

Further, the satellites are in high orbits, where the curvature of spacetime due to the Earth's mass is less than it is at the Earth's surface. A prediction of General Relativity is that clocks closer to a massive object will seem to tick more slowly than those located further away (see Lecture 20 on Black Holes). As such, when viewed from the surface of the Earth, the clocks on the satellites appear to be ticking faster than identical clocks on the ground. A calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day.

The combination of these two relativitic effects means that the clocks on-board each satellite should tick faster than identical clocks on the ground by about 38 microseconds per day (45-7=38)!

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#### Ich

yogi said:
To answer the question, you will need to know how one twin acquired motion wrt to the other
That´s nonsense. Neglecting gravity, the twin staying in an inertial frame will age faster, no matter how he got there.
So the twin on earth will age slower.

#### professor

you know what i cant make up my mind....nvmd im pretty sure i agree that that is not nonesense though

yes... now i am sure without gravity on earth... you would be right, but earth is moving relativley slow compared tot he speed of light, and we would not see a great amount of velovity induced time diation... now suppose you stop mars from moving, and put one twin on there... and your speculation would be correct... otherwise, i agree with the big guy up there (the one with like 2000 posts, forgot his name by now)

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