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)

Question

Responses

about 1 year
about 1 year

about 2.5 years
about 2.5 years

about 7.5 years
about 7.5 years

about 22.5 years
about 22.5 years

Answer 1

To determine how long it would take to reach Mars, we first need to calculate the distance to Mars based on the information provided.

1. Distance to the Moon: 386,400 km
2. Distance to Mars at its closest: 140 times the distance to the Moon

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

Next, we consider the time it takes to reach the Moon, which is given as 3 days.

3. Speed of the spaceship: To find the speed, we use the distance to the Moon and the time taken: \[ \text{Speed} = \frac{\text{Distance to the Moon}}{\text{Time to reach the Moon}} = \frac{386,400 \text{ km}}{3 \text{ days}} = 128,800 \text{ km/day} \]

4. Time to reach Mars: Now that we have the speed, we can calculate the time it would take to reach Mars: \[ \text{Time to reach Mars} = \frac{\text{Distance to Mars}}{\text{Speed}} = \frac{54,096,000 \text{ km}}{128,800 \text{ km/day}} \approx 420 \text{ days} \]

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

Since "about 1 year" is the closest option provided, the answer is: about 1 year.