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 1 year about 1 year about 7.5 years about 7.5 years about 2.5 years about 2.5 years about 22.5 years

Answer 1

To find out how long it would take the spaceship to reach Mars based on the given information, we first calculate its speed to the moon.

The distance to the moon is 386,400 km, and the spaceship takes 3 days to make that journey. We can find the speed as follows:

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

Converting 3 days into hours: 3 days = 3 × 24 hours = 72 hours

Now, substituting into the speed formula:

\[ \text{Speed} = \frac{386,400 \text{ km}}{72 \text{ hours}} \approx 5,366.67 \text{ km/hour} \]

Next, we find the distance to Mars. If the distance to Mars is about 140 times the distance to the moon, we can calculate this distance:

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

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

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

To convert hours into days:

\[ \text{Time in days} = \frac{10,080 \text{ hours}}{24 \text{ hours/day}} \approx 420 \text{ days} \]

Finally, converting days into years:

\[ \text{Time in years} = \frac{420 \text{ days}}{365 \text{ days/year}} \approx 1.15 \text{ years} \]

Thus, the approximate time it would take for the spaceship to reach Mars is about 1 year.