A voyager forever voyaging

The Voyager 1 spacecraft is currently about 18.5 billion km from the Earth. How long does it take in seconds for a radio signal to get from Voyager 1 to Earth?

Details and assumptions

  • The speed of light is 3 × 1 0 8 m/s 3 \times 10^8~\mbox{m/s} .


The answer is 61667.

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10 solutions

Andhika Rahardian
Oct 21, 2013

First of all , we must change from 18.5 18.5 billion km to m , and we got 18.5 18.5 trillion m

or 1.85 × 1 0 13 m 1.85 \times 10^{13} m

the question is how long does it take in seconds ,it means we must find "time." ( T T )

T = s v T=\frac {s}{v} , radio signal speed = speed of light so , we can write

T = 1.85 × 1 0 13 m 3 × 1 0 8 m / s T=\frac {1.85 \times 10^{13} m}{3 \times 10^{8} m/s}

cause the unit must be seconds , we can eliminate meter unit. meter/meter equals 1 so

T = 1.85 × 1 0 13 3 × 1 0 8 1 / s T=\frac {1.85 \times 10^{13}}{3 \times 10^{8} 1/s}

T = 0.61667 × 1 0 5 1 s T=\frac {0.61667 \times 10^{5}}{\frac{1}{s}} , T = 61667 s T= 61667 s , so the answer is 61667 \boxed{61667}

Does anyone know what useful science Voyager 1 is still reporting back (at a time delay of 61667 seconds of course...)?

David Mattingly Staff - 7 years, 7 months ago
Adi Pratama
Dec 21, 2013

s = 18.5 billion km.

c = 3 x 10^8 m/s.

t = s/c

t = 18.5 billion km / (3 x 10^8 m/s).

t = 61666.667 s

Yaar ye million billion kyu de dete hai confusing

Abhishek Kashyap - 7 years, 5 months ago

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yes millions and billions is quite confusing

Ravalee Kanthi Ravuri - 7 years, 4 months ago

Million billion tak to thik hai, answer exact mangte hain. Lag raha hai jaise copy pen saath mein leke baithe honge calculate karne k liye.

Prakhar Dwivedi - 5 years, 1 month ago

It is widely known that S p e e d = D i s t a n c e T i m e Speed = \tfrac{Distance}{Time} . After a mere substitution, we get that 3 1 0 8 m / s = 18.5 1 0 9 1 0 3 m X s X = 61667 s 3 * 10^8 m/s = \dfrac{18.5 * 10^9 * 10^3 m}{X s} \Rightarrow X = 61667 s .

well done...:)

Vishal Sanghani - 7 years, 5 months ago

hi

amith vamsi - 7 years, 7 months ago
Noel Quirol
Oct 20, 2013

time = distance/rate

1.85x10^9 km = 1.85x10^13m

t = 1.85x10^13m/ 3x10^8 m/s = 0.6166 x 10^5 = 6.166 x 10^5

Karen Adelan
Mar 9, 2014

just only a simple problem... to get the right answer you must need to know conversion method

Ícaro Magalhães
Jan 11, 2014

18.5 billion km = 18.500.000.000 km = 18.500.000.000.000 m

3x10^8 m/s = 300.000.000 m/s

18.500.000.000.000 m / 300.000.000 ms = 61666.66667 s

Raunaq Ahmed
Jan 8, 2014

time = distance / speed , time = (18.5E12) / 3E8 = 61667.667

Budi Utomo
Dec 24, 2013

We must know if t = s/v, so t = 18.5 x 10^12 m / 3 x 10^8 m/s = 61666,66667 seconds = 6.1667E+4 (ANSWER)

Ayon Pal
Oct 23, 2013

T i m e = D i s t a n c e S p e e d Time = \frac{Distance}{Speed}

So, there is Total Distance = 18.5 1 0 9 k m 18.5 1 0 12 m 18.5 * 10^9 km \implies 18.5 * 10^{12} m

And, Speed = 3 1 0 8 m / s 3 * 10^8 m/s

So, total time is second it will take = 18.5 1 0 12 3 1 0 8 61667 \frac{18.5 * 10^{12} }{3 * 10^8} \implies 61667 s [approx]

Darryl Yeo
Oct 21, 2013

We need to convert 18.5 billion km to seconds. We already have a rate to convert it–the speed of light.

18.5 × 1 0 9 k m × 1 s e c 3 × 1 0 8 m = 18.5 \times 10^{9} km \times \frac{1 sec}{3 \times 10^{8} m} =

18.5 × 1 0 9 k m × 1 s e c 3 × 1 0 5 k m = 18.5 \times 10^{9} km \times \frac{1 sec}{3 \times 10^{5} km} =

18.5 × 1 0 9 s e c 3 × 1 0 5 = \frac{18.5 \times 10^{9} sec}{3 \times 10^{5}} =

18.5 3 × 1 0 9 1 0 5 s e c = \frac{18.5}{3} \times \frac{10^{9}}{10^{5}} sec =

6.1667 × 1 0 4 s e c = 6.1667 \times 10^{4} sec =

61667 s e c \boxed{61667 sec}

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