To calculate the time it would take for the gamma radiation wave to reach Earth, we need to convert the distance from light-years to kilometers and then divide it by the speed of the wave.
Given: Distance = 8000 light years Speed of the wave = 12,000 km/h
1 light year is the distance light travels in one year, approximately equal to 9.461 trillion kilometers. So, we can calculate the distance in kilometers as follows:
Distance = 8000 light years * 9.461 trillion km/light year
Now we can calculate the time it would take for the wave to reach Earth:
Time = Distance / Speed
Let's plug in the values and calculate:
Distance = 8000 light years * 9.461 trillion km/light year ≈ 75.6888 trillion km
Time = 75.6888 trillion km / 12,000 km/h
Time ≈ 6.3074 billion hours
Since this is a very long time, let's convert it to a more practical unit:
Time ≈ 6.3074 billion hours / 24 hours/day ≈ 262.8 million days
Therefore, it would take approximately 262.8 million days for the gamma radiation wave to reach Earth.