A human-operated spaceship reaches the moon in 3 days. The moon is about 386,400 km from Earth. Mars, our closest planetary neighbor, is, at its closest, about 140 times farther away from us than the moon if Mars stays in place. Assuming a very simple model of the solar system, about how long would it take that same spaceship to reach Mars?(1 point)

Responses

about 2.5 years
about 2.5 years

about 7.5 years
about 7.5 years

about 22.5 years
about 22.5 years

about 1 year

1 answer

To find out how long it would take the spaceship to reach Mars, we can start by calculating the distance to Mars based on the information given.

The distance to the Moon is about 386,400 km. If Mars is about 140 times farther away than the Moon, we can calculate the distance to Mars as follows:

\[ \text{Distance to Mars} = 140 \times 386,400 \text{ km} = 54,096,000 \text{ km} \]

Next, we determine the speed of the spaceship. The spaceship took 3 days to reach the Moon, which is 386,400 km away. First, convert 3 days into hours:

\[ 3 \text{ days} = 3 \times 24 \text{ hours} = 72 \text{ hours} \]

Now, calculate the speed of the spaceship in kilometers per hour:

\[ \text{Speed} = \frac{\text{Distance to Moon}}{\text{Time to Moon}} = \frac{386,400 \text{ km}}{72 \text{ hours}} \approx 5,366.67 \text{ km/h} \]

Now, we can calculate the time it would take to reach Mars using the following formula:

\[ \text{Time to Mars} = \frac{\text{Distance to Mars}}{\text{Speed}} = \frac{54,096,000 \text{ km}}{5,366.67 \text{ km/h}} \approx 10,080 \text{ hours} \]

To convert hours into years, we can use the following conversions:

\[ \text{Years} = \frac{10,080 \text{ hours}}{24 \text{ hours/day} \times 365 \text{ days/year}} \approx 1.15 \text{ years} \]

Therefore, the answer is roughly about 1 year.

So the correct response is: about 1 year.