Final answer:
It takes approximately 5.46 hours for a message to travel from Earth to a spacecraft on Pluto when using the speed of light in kilometers per hour provided.
Step-by-step explanation:
You asked how long it takes for a message to travel from Earth to a spacecraft on Pluto at its average distance from Earth, which is about 5.9 billion kilometers (approximately 32 astronomical units, AU). To answer this question, we need to use the speed of light in a vacuum, which is approximately 299,792 kilometers per second (km/s), or in the units given for your question, 1.08 × 10⁹ km/hr.
First, we must convert the average distance from kilometers to astronomical units because this is the unit given in the question. 1 AU is about 150 million kilometers. So, 5.9 billion kilometers is equivalent to 5.9 billion km ÷ 150 million km/AU = 39.33 AU.
Now let's calculate the time it takes for light to travel 39.33 AU. We will use the speed of light given in the question.
- Convert the speed of light to kilometers per second — this is 1.08 × 10⁹ km/hr ÷ 3600 seconds/hr = 300,000 km/s.
- Calculate the time — 39.33 AU × 150 million km/AU ÷ 300,000 km/s = 19,665 seconds.
- Convert the time from seconds into hours — 19,665 seconds ÷ 3600 seconds/hr = 5.46 hours.
So, a message would take approximately 5.46 hours to travel from Earth to a spacecraft on Pluto at its average distance.