How Does Time Dilation Affect the Voyager 1 Space Probe?

[Stratosphere]

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 don't know how to get answer (b)

 

[Doc Al]

What's the time dilation formula?

 

[Stratosphere]

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

 

[Doc Al]

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"

 

[Stratosphere]

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

 

[Doc Al]

$$\Delta t = \gamma(\Delta + v\Delta /c^2)$$

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.

 

[Stratosphere]

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

 

[Stratosphere]

If that's the right formula I think I got the right answer, T= 31000000.05 seconds have passed for the 31000000 seconds on earth.

 

[Briggs]

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]

If that's 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.

 

[Stratosphere]

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

 

[Doc Al]

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

 

[Stratosphere]

.05 seconds?

 

[Doc Al]

.05 seconds?

Sounds good.