# Time Dilation relativity

## Homework Statement

The Voyager 1 space probe, launched in 1977, is moving faster
relative to the earth than any other human-made object, at 17,000
meters per second.
(a) Calculate the probe's
. p
(b) Over the course of one year on earth, slightly less than one year
passes on the probe. How much less?

## Homework Equations

$$\gamma$$=1/$$\sqrt{}1-(v/c)^2$$

## The Attempt at a Solution

I calculated the $$\gamma$$ but i dont know how to get answer (b)

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Doc Al
Mentor
What's the time dilation formula?

What it says for the formula. On my first post.$$\gamma$$=1/$$\sqrt{}1-(v/c)^2$$

Doc Al
Mentor
What it says for the formula. On my first post.$$\gamma$$=1/$$\sqrt{}1-(v/c)^2$$
That's just the definition of gamma, a factor that appears in many relativistic formulas. What's the formula for time dilation? (It will certainly involve gamma, but also T and T'.)

Look here: https://www.physicsforums.com/showpost.php?p=905669&postcount=3"

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$$\Delta t = \gamma(\Delta + v\Delta /c^2)$$
By the way what does $$\Delta$$ mean?

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Doc Al
Mentor
$$\Delta t = \gamma(\Delta + v\Delta /c^2)$$
That's not the one you want. (Look for "time dilation".)
By the way what does $$\Delta$$ mean?
Δ means "change"; Δt represents a time interval.

$$T$$=$$\frac{}{}t/\sqrt{}1-(v/c)^{}2$$
This is the one in my text book.

If thats the right formula I think I got the right answer, T= 31000000.05 seconds have passed for the 31000000 seconds on earth.

I think you have the values of T and t_0 mixed up. Remember time dilation would mean that slightly less time passes for the probe.

Doc Al
Mentor
If thats the right formula I think I got the right answer, T= 31000000.05 seconds have passed for the 31000000 seconds on earth.
Yes, it looks like you mixed things up. The rule to remember is that moving clocks run slow by a factor of gamma. Viewed from earth, the earth clocks read a longer time than does the moving probe clock.

Since the speed is quite a bit less than c, I suggest using a binomial approximation for gamma.

So i just redid it and i got 30,999,999.95 seconds passed on the probe. Is that right?

Doc Al
Mentor
Figure out how many fewer seconds passed on the probe, not the total number of seconds.

.05 seconds?

Doc Al
Mentor
.05 seconds?
Sounds good.