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 22.5 years
about 22.5 years

about 7.5 years
about 7.5 years

about 2.5 years
about 2.5 years

about 1 year
about 1 year

1 answer

To find out how long it would take the spaceship to reach Mars, we can start with the given information about the distance to the moon and the travel time to get there:

  1. Distance to the Moon: 386,400 km
  2. Travel time to the Moon: 3 days

First, we can determine the speed of the spaceship:

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{386,400 \text{ km}}{3 \text{ days}} \]

To express speed in km per day:

\[ \text{Speed} = \frac{386,400 \text{ km}}{3} \approx 128,800 \text{ km/day} \]

Next, we find the distance to Mars at its closest approach, which is about 140 times the distance to the moon:

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

Now, we can calculate the time it would take to reach Mars at the same speed:

\[ \text{Time to Mars} = \frac{\text{Distance}}{\text{Speed}} = \frac{54,096,000 \text{ km}}{128,800 \text{ km/day}} \approx 420 \text{ days} \]

To convert days into years:

\[ 420 \text{ days} \approx \frac{420}{365} \approx 1.15 \text{ years} \]

Thus, based on this calculation, the closest approximation from the given options is:

about 1 year.