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

Answer 1

To find out how long it would take to reach Mars based on the travel time to the Moon, we can follow these steps:

1. Distance from Earth to the Moon: 386,400 km
2. Distance from Earth to Mars (at closest approach): 140 times the distance to the Moon.

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

3. Travel time to the Moon: 3 days.

4. Convert days to hours: \[ 3 \text{ days} = 3 \times 24 \text{ hours} = 72 \text{ hours} \]

5. Speed of the spaceship: To find the speed, we can use the distance to the Moon and the time it takes: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{386,400 \text{ km}}{72 \text{ hours}} \approx 5,366.67 \text{ km/h} \]

6. Calculate the time to reach Mars: Using the same speed for the distance to Mars: \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{54,096,000 \text{ km}}{5,366.67 \text{ km/h}} \approx 10,080 \text{ hours} \]

7. Convert hours to years: \[ 10,080 \text{ hours} = \frac{10,080}{24 \times 365.25} \approx 1.15 \text{ years} \]

So, the closest response option is about 1 year.