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Pioneer space probe moving at a speed of $30km/s$. Assuming its heading for Proxima Centauri, which is situated at $4.2ly$ from earth, calculate how long it would take to get there in years, to the nearest year?

Could you please help.

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According to Google: 41 971 years –  Asad Nov 28 '13 at 12:36
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closed as off-topic by Emilio Pisanty, Dimensio1n0, jinawee, John Rennie, akhmeteli Nov 28 '13 at 16:37

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2 Answers

Hints:

  • $30 \,km \, s^{-1}$ is about $\dfrac{1}{10000}$ times the speed of light and more precisely $\dfrac{30000}{299792458}$ times
  • Distance of $4.2$ light years

  • Number of years neded is ...

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1 year is approximately $y = 3.15 \times 10^7 s$, and light travels at $c = 3.00\times 10^5 km/s$, so convert the speed of the space probe in km/s into ly/s and then into ly/y.

Note that $\frac{km}{s} = \frac{km}{s} \left(\frac{3.15 \times 10^7s}{1 y}\right) \times \left(\frac{ly}{3.00\times 10^5 km/s \times 3.15 \times 10^7s}\right) = \frac{1}{30.0\times 10^4} \frac{ly}{y}$

You should be able to take it from here...

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