Answer:
Time = 9.0252 *10^12 s
Step-by-step explanation:
Given:
- The distance from Earth to Alpha Centauri = 4.3 light years
- The distance from Earth to Sirius = 8.6 light years
- Speed of the probe is V = 18.03 km/s
- 1 AU = 1.58125 x 10-5 light-years
Find:
How long will the probe have been traveling from when it first leaves Earth to when it arrives at Sirius?
Solution:
- We will track probe for each destination it reaches one by one:
Earth ------> Alpha Centauri d_1 = 4.3 light years
Alpha Centauri ------> Earth d_2 =4.3 light years
Earth ------> Sirius d_3 = 8.6 light years
Total distance D = 17.2 light years.
- Now we know the total distance traveled by the probe is D. We will convert the distance into km SI units:
1 AU ------------------> 1.58125 x 10-5 light-years
x AU ------------------> 17.2 light years.
- Using direct proportions
x = 17.2 / (1.58125 x 10-5) = 1087747.036 AU
Also,
1 AU ---------------------> 149597870700 m
1087747.036 AU ----> D m
- Using direct proportions
D = 1087747.036*149597870700 = 1.62725*10^17 m
- Now use the speed - distance - time formula to compute the total time taken:
Time = Distance traveled (D) / V
Time = 1.62725*10^17 / 18.03*10^3
Answer: Time = 9.0252 *10^12 s
