# Do we have to worry about relativity when studying galactic objects?

*I'm puzzled by the implication of the Einstein's theory about time
being in a way a function of speed and/or acceleration. Doesn't it
mean that time must be actually different on the bodies with different
speed if this speed is big enough to notice it? Might be not
noticeable on Mars compared to Earth, since the rotation of the Solar
System probably compensates or balances somehow and their speed isn't
big anyway. But what about time in the whole of the Solar System which
rotates with a really huge speed around the centre of the Galaxy
compared to time around Antares? What about time in our Local Group
compared to the time in the M83, for instance, ot M31? *

You ask a good question; it turns out that astronomers do have to worry about the time effects implied by Einstein's theories in certain circumstances.

As you mention, the time measured by an observers in two different reference frames depends on their relative speeds; in short, an observer that is observing an event in a reference frame moving at speed v will measure the time in that frame to move slower than in his frame by a factor gamma=square root of (1-(v/c)squared), where c is the speed of light. So, we only need to worry about these effects when (v/c) squared is comparable to 1. To be safe, let's assume that no correction is needed is v is 20% the speed of light.

Now, the
speed of light is 300000 km/s, and so only objects with
velocities of 60 000 km/s relative to the Earth need to take relativity
into account. The Solar system does move quickly around the galactic
centre by Earth standards at 220 km/s, but this is nowhere near fast
enough to require a correction for relativistic effects. So, the speed
with which time elapses in the Solar System and in Antares are very, very
nearly the same.
Astronomers do have to worry about these relativistic effects when
studying so called "high energy phenomena" in the Universe, however. A
good example is in the study of jets that are emitted in the vicinity of
black holes, both at the centre of distant galaxies and in stellar systems
in the solar neighbourhood. These jets are often observed to propagate
through the interstellar medium in these systems at substantial fractions
of the speed of light (some are even observed to move *faster* than c, but
this is just an illusion caused by relativity). Estimates of the
propagation speed and energetics of the jets may require substantial
corrections for relativistic effects. Look here for a pretty picture of a jet in a nearby galaxy.

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