Final answer:
The total time for a message to travel from Earth to the New Horizons probe when it was at Pluto and back would be around 17.78 hours. The New Horizons probe was about 32 AU from Earth in July 2015, and with the speed of light being 1.08 × 10⁹ km/hr, it would take approximately 8.89 hours one way.
Step-by-step explanation:
If a radio message was sent today from Earth to the New Horizons space probe and a reply was sent back immediately, we would have to wait for the time it takes the message to travel to New Horizons and for the reply to travel back. This duration is dependent on the distance between Earth and the spacecraft and the speed of light. In July 2015, when New Horizons flew by Pluto, Pluto was approximately 32 astronomical units (AU) from Earth. One AU is the average distance from the Earth to the Sun, which is about 150 million km (or 93 million miles).
The speed of light is approximately 1.08 × 10⁹ km/hr. To calculate the time it takes for a radio message to travel one AU, you would divide this distance by the speed of light. Since the distance to New Horizons will change as it travels, we'll use the distance at the time of the Pluto flyby for this estimation.
The time for the radio message to travel to New Horizons and back, covering 64 AU (32 AU each way), can be calculated as follows:
(150 million km × 64) / (1.08 × 10⁹ km/hr)
This calculation will give us the total time in hours, which can be converted into other time units as needed to find the answer. In this case, the round-trip communication time is approximately 8.89 hours each way, totaling around 17.78 hours, which is roughly equivalent to 'Option E': 9 hours, but considering it's a round trip, it takes longer than 9 hours.