14. The nearest star, Proxima Centauri is 4.0 x 10 km away. Calculate the time it takes light signal from the earth to the star? How many years will it take a spacecraft travelling with speed of 0.0001c to reach Proxima Centauri. (c = 3 x 10 ms).
Answers
Answer:
Light travels 9.46x10^12km in a year. This is the standard measure of galactic distance, the light year. So proxima is 4.244 ly away. And that is length of time a light signal would take to reach us from there, 4 years and a smidgeon under three months.
Your spaceship is moving at 0.0001c so it will take 4.244/0.0001 years, 42,440 years.
Answer:
4.22 x 10^9 years or approximately 4.22 billion years.
Explanation:
To calculate the time it takes for light to reach Proxima Centauri from Earth:
Distance between Earth and Proxima Centauri = 4.0 x 10^13 km
Speed of light, c = 3 x 10^5 km/s
Using the formula:
time = distance/speed
Time taken for light to reach Proxima Centauri = (4.0 x 10^13 km)/(3 x 10^5 km/s) = 1.33 x 10^8 seconds or approximately 4.22 years (since 1 year = 31,536,000 seconds)
To calculate the time it will take a spacecraft travelling with a speed of 0.0001c to reach Proxima Centauri:
Speed of spacecraft, v = 0.0001c
Distance between Earth and Proxima Centauri = 4.0 x 10^13 km
Using the formula: time = distance/speed
Time taken for spacecraft to reach Proxima Centauri = (4.0 x 10^13 km)/(0.0001c) = (4.0 x 10^13 km)/(0.0001 x 3 x 10^5 km/s) = 1.33 x 10^17 seconds
To convert this into years, we divide by the number of seconds in a year:
Time taken for spacecraft to reach Proxima Centauri = (1.33 x 10^17 seconds)/(31,536,000 seconds/year) =
4.22 x 10^9 years or approximately 4.22 billion years.
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