NASA is sending a probe to Alpha Centauri and then to Sirius. A problem with the probe is noticed while it is at Alpha Centauri, so it must go back to Erth before going to Sirius. Alpha Centauri is 4.3 light-years away from Earth and Sirius is 8.6 light-years away. The probe is traveling at 18.03 km/s, there are 1.58125 x 10-5 light-years in one astronomical unit. How long will the probe have been traveling from when it first leaves Earth to when it arrives at Sirius?
Answers
Given : NASA is sending a probe to Alpha Centauri and then to Sirius. A problem with the probe is noticed while it is at Alpha Centauri, so it must go back to Erth before going to Sirius. Alpha Centauri is 4.3 light-years away from Earth and Sirius is 8.6 light-years away. The probe is traveling at 18.03 km/s,
To Find : How long will the probe have been traveling from when it first leaves Earth to when it arrives at Sirius?
Solution:
Earth to Alpha Centauri = 4.3 light-years
Alpha Centauri to Earth = 4.3 light-years
Earth to Sirius = 8.6 light-years
Total Distance covered = 4.3 + 4.3 + 8.6 = 17.2 light years
1 light year = 9.461 x 10¹² km
Total Distance = 17.2 x 9.461 x 10¹²
= 162.7292 x 10¹² km
Speed = 18.03 km/s,
=> Time = distance / Speed
=> Time = 162.7292 x 10¹² / 18.03 Sec
= 9.025 x 10¹² secs
= 9.025 x 10¹² / 3600 hrs
= 2.507 x 10⁹ hrs
= 2.507 x 10⁹ / (365 x 24 ) years
= 2.8618 x 10⁵ years
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