Light (or radio waves) takes approximately 8 minutes and 20 seconds to travel from the Sun to Earth. In the future, if a human colony orbits Saturn, how long will it take to send a message from Earth to that colony? A. 71.25 seconds B. 79.58 seconds C. 1 hour, 19 minutes, 35 seconds D. 1 hour, 11 minutes, 15 seconds

To calculate the time it takes for a message to travel from Earth to a human colony orbiting Saturn, we need to consider the distance between Earth and Saturn when they are at their closest approach, also known as opposition.

The average distance between Earth and Saturn is about 1.2 billion kilometers (746 million miles). However, this distance can vary significantly due to the elliptical orbits of Earth and Saturn. At their closest approach, the distance can be around 1.2 billion kilometers.

Light (or radio waves) travels at a constant speed of approximately 299,792 kilometers per second in a vacuum.

To find the time it takes for a message to travel from Earth to Saturn at their closest approach:

Distance = 1.2 billion kilometers

Speed of light = 299,792 kilometers per second

Time = Distance / Speed of light

Time = 1,200,000,000 km / 299,792 km/s

Time ≈ 4,001 seconds

This is the one-way travel time from Earth to Saturn when they are at their closest approach.

Since the message has to travel from Earth to the colony and back to Earth, the total round trip time would be double this one-way travel time:

Round trip time = 2 * 4,001 seconds

Round trip time ≈ 8,002 seconds

Now, let's convert this total round trip time from seconds to a more readable format:

8,002 seconds ≈ 2 hours, 13 minutes, 22 seconds

Therefore, the approximate time it would take to send a message from Earth to a human colony orbiting Saturn and receive a response back to Earth would be approximately 2 hours, 13 minutes, and 22 seconds. None of the options provided exactly matches this calculation, but the closest one is:

D. 1 hour, 11 minutes, 15 seconds (which is not accurate based on the calculation).