In 2003, NASA launched the rover Spirit onto the surface of Mars to explore our planetary neighbor. Near the end of January 2010, Mars was 99.33 million km away from Earth. Assume the speed of communication is at the speed of light, which is 300,000,000 m/s. If a researcher on Earth requested information from Spirit about its temperature, how long did the researcher have to wait for a reply after sending the request? Express your answer in the form minutes and seconds.
one-way trip delay:
(99.33*10^6km)/(3*10^5km/s) = 33.11*10 = 333.1 seconds
Now just convert that to minutes & seconds.
To calculate the time it takes for the researcher to receive a reply from the Spirit rover on Mars, we need to determine the time it takes for the communication signal to travel from Earth to Mars, and then multiply it by two since the round trip needs to be accounted for.
The distance between Earth and Mars at the specified time is 99.33 million km. We can convert this distance into meters by multiplying it by 1,000,000 (since there are 1,000,000 meters in a kilometer).
Distance = 99.33 million km * 1,000,000 m/km = 99.33 * 10^12 m
Now, to calculate the time it takes for the signal to travel, we divide the distance by the speed of light:
Time = Distance / Speed = (99.33 * 10^12 m) / (300,000,000 m/s)
Time = 331,000 seconds
Since this is the time for the one-way trip, we need to multiply it by 2 to calculate the round trip time:
Round Trip Time = 2 * 331,000 seconds = 662,000 seconds
To convert this time into minutes and seconds, we divide the total seconds by 60 to get the number of minutes and take the remainder as the number of seconds:
Minutes = 662,000 seconds / 60 seconds/minute ≈ 11,033 minutes
Seconds = 662,000 seconds % 60 seconds/minute = 20 seconds
So, the researcher would have to wait approximately 11,033 minutes and 20 seconds for a reply from the Spirit rover.