An advanced space probe in the twenty-first century travelsfrom the earth with a

Question

An advanced space probe in the twenty-first century travelsfrom the earth with a speed of 5.00 x 106 m/s relativeto the earth and then returns at the same speed. The probe carriesan atomic clock that has been carefully synchronized with anidentical clock that remains at rest on the earth. The probereturns after 1 year, as measured on earth, has passed. (a) What is the difference in the elapsed times on the twoclocks? (b) Which clock, the one in the probe or the one on earth,shows the smallest elapsed time? An advanced space probe in the twenty-first century travelsfrom the earth with a speed of 5.00 x 106 m/s relativeto the earth and then returns at the same speed. The probe carriesan atomic clock that has been carefully synchronized with anidentical clock that remains at rest on the earth. The probereturns after 1 year, as measured on earth, has passed. (a) What is the difference in the elapsed times on the twoclocks? (b) Which clock, the one in the probe or the one on earth,shows the smallest elapsed time?

Explanation / Answer

An advancedspace probe in the twenty-first century travels from the earth witha speed of 5.00 x 106 m/s relative to the earth and thenreturns at the same speed. The probe carries an atomic clock thathas been carefully synchronized with an identical clock thatremains at rest on the earth. The probe returns after 1 year, asmeasured on earth, has passed.

(a) What isthe difference in the elapsed times on the twoclocks?
     {Time Difference} =
          = {Earth Elapsed Time} - {Probe ElapsedTime}
         = (Time, Earth) - (Time, Earth)*(1 - (v/c)^2)^(1/2)
          = (1 year) - (1 year)*(1 - ((5.0e+6)/(3.0e+8))^2)^(1/2)
          = (1year) - (1 year)*(0.9998611016)
          = (1year)*(1.0 - 0.9998611016)
          = (365)*(24)*(60)*(60)*(1.0- 0.9998611016)
          = 4380.3 sec

(b) Whichclock, the one in the probe or the one on earth, shows the smallestelapsed time?
     {Smallest Elapsed Time} = {PROBE Clock}

.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.