We start with
Next, we can factor out the term on the right side
Now, we will substitute back
resulting in
So,
.............Response
Answer: 942
Detailed explanation: this was quite challenging!
After 1 hour >> 44 miles apart
after 2 hours >> 88 miles apart
after 2.5 hours >> 110 miles apart
Two and a half hours
Total time taken = 9.0252 *10^12 s.
Step-by-step explanation:
Data provided:
- Distance from Earth to Alpha Centauri: 4.3 light years.
- Distance from Earth to Sirius: 8.6 light years.
- Probe speed: V = 18.03 km/s.
- 1 AU equals 1.58125 x 10^-5 light-years.
Objective:
Determine the total time the probe has been in motion from leaving Earth to reaching Sirius.
Solution:
- Journey is tracked for each destination sequentially:
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
Sum of distances = D = 17.2 light years.
- Now, we convert the total distance into kilometers (SI units):
1 AU ----------> 1.58125 x 10^-5 light-years
x AU ----------> 17.2 light years.
- By proportions:
x = 17.2 / (1.58125 x 10^-5) = 1087747.036 AU.
Also,
1 AU ---------------------> 149597870700 m
1087747.036 AU ----> D m.
- Using proportions:
D = 1087747.036*149597870700 = 1.62725*10^17 m.
- Finally, applying the speed-distance-time formula:
Time = Distance traveled (D) / V
Time = 1.62725*10^17 / (18.03*10^3).
Final answer: Time = 9.0252 *10^12 s.
