The distnace from earth to the moon is 239,000 miles.
a. how many kilometers are in 239000 miles?
b. given that the light travels at 3.00*10^8 m/s , how many minutes does it take for light to travel to the moon ?
c. The apollo 10 mission holds the record for the highest speed by a manned vehicle at 11080 m/s . How many minutes would it take for the apollo 10 mission to reach the moon assuming the rocket travels ina straight line at that top speed?
d. The apollo 11 mission took 73.45 hours to reach lunar orbit once it left earths orbit. The avergae speed duirng that time was 5500km/hr. How many miles did the apollo 11 mission actually travel in space ?
The Correct Answer and Explanation is :
Let’s break this down step by step.
a. Convert the distance from miles to kilometers.
To convert miles to kilometers, we use the conversion factor:
1 mile = 1.60934 kilometers.
So, for 239,000 miles:
[
239,000 \, \text{miles} \times 1.60934 = 384,405.66 \, \text{kilometers}
]
Thus, the distance from Earth to the Moon is approximately 384,406 kilometers.
b. Time for light to travel to the moon
The speed of light is given as (3.00 \times 10^8) m/s. First, we need to convert the distance from kilometers to meters since the speed of light is in meters per second.
We know:
[
1 \, \text{km} = 1000 \, \text{m}
]
So, the distance to the moon in meters is:
[
384,406 \, \text{km} \times 1000 = 384,406,000 \, \text{m}
]
Now, we calculate the time it takes for light to travel this distance:
[
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{384,406,000 \, \text{m}}{3.00 \times 10^8 \, \text{m/s}} = 1.281 \, \text{seconds}
]
To convert seconds to minutes, we divide by 60:
[
\text{Time in minutes} = \frac{1.281 \, \text{seconds}}{60} = 0.02135 \, \text{minutes}
]
Thus, it takes approximately 0.02135 minutes (or about 1.28 seconds) for light to travel from Earth to the Moon.
c. Time for the Apollo 10 mission to reach the moon
The Apollo 10 mission traveled at a top speed of 11,080 m/s. To calculate how long it would take for the mission to travel to the moon at this speed, we first need to use the distance in meters:
The distance from Earth to the Moon is:
[
384,406,000 \, \text{m}
]
Now, we use the formula for time:
[
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{384,406,000 \, \text{m}}{11,080 \, \text{m/s}} = 34,696.5 \, \text{seconds}
]
To convert seconds into minutes:
[
\text{Time in minutes} = \frac{34,696.5 \, \text{seconds}}{60} = 578.27 \, \text{minutes}
]
So, it would take 578.27 minutes (or about 9.64 hours) for Apollo 10 to reach the Moon traveling at its top speed.
d. Distance traveled by Apollo 11 mission
We are told that the Apollo 11 mission took 73.45 hours to reach lunar orbit and traveled at an average speed of 5500 km/hr. To find the distance traveled, we use the formula:
[
\text{Distance} = \text{Speed} \times \text{Time}
]
Converting the time into hours:
[
\text{Distance} = 5500 \, \text{km/hr} \times 73.45 \, \text{hr} = 403,975 \, \text{km}
]
Now, to convert kilometers to miles:
[
1 \, \text{km} = 0.621371 \, \text{miles}
]
Thus:
[
403,975 \, \text{km} \times 0.621371 = 251,888.52 \, \text{miles}
]
Therefore, the Apollo 11 mission traveled approximately 251,889 miles.
Summary of Results:
- The distance from Earth to the Moon is about 384,406 kilometers.
- It takes light 0.02135 minutes (1.28 seconds) to travel to the Moon.
- The Apollo 10 mission would take about 578.27 minutes to reach the Moon at its top speed of 11,080 m/s.
- The Apollo 11 mission traveled approximately 251,889 miles to reach lunar orbit, covering the distance in 73.45 hours at an average speed of 5500 km/h.