Question

When the Voyager I and Voyager II spacecraft were exploring the outer planets, NASA flight controllers had to plan the crafts' moves well in advance. How many seconds elapse between the time a command is sent from Earth and the time the command is received by Voyager at Neptune? Assume the distance from Earth to Neptune is 4.76E+12 m.

Answer 1

Approximately 15,866,667 seconds (or about 186 days) elapse between the time a command is sent from Earth and the time the command is received by Voyager at Neptune.

Step-by-step explanation:

In order to estimate the time lapse between sending a command from Earth and receiving it at Voyager at Neptune, we need to calculate the time it takes for the radio signal to travel the distance between the two. The distance from Earth to Neptune is approximately 4.76E+12 m. The speed of light in a vacuum is about 3.00E+8 m/s. Using the formula distance = speed x time, we can rearrange the formula to solve for time: time = distance / speed. Plugging in the values, we find that it takes approximately 15866666.7 seconds for a command to reach Voyager at Neptune.

Answer 2

`1.59*10^4 s`

Step-by-step explanation:

The signals sent from the earth, travel at the speed of light, therefore the travel time of the signal between the earth and neptune, can be calculated with the following equation, which relates time, speed and distance:

`t=(x)/(v)\\t=(4.76*10^(12) m)/(3*10^8 m/s)=1.59*10^4 s\\`

The time elapsed is approximately 4.41 hours