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

Answer 1

To determine how long it would take a spaceship to reach Mars using the given information, we can follow these steps:

1. Distance from Earth to Moon: 386,400 km
2. Time taken to reach the Moon: 3 days
3. Distance from Earth to Mars: \( 386,400 \text{ km} \times 140 = 54,096,000 \text{ km} \)

Next, we calculate the speed of the spaceship:

• Speed = Distance / Time
• Time taken to reach the Moon in hours: \( 3 \text{ days} \times 24 \text{ hours/day} = 72 \text{ hours} \)
• Speed = \( 386,400 \text{ km} / 72 \text{ hours} \approx 5,366.67 \text{ km/hour} \)

Now, we can find the time taken to reach Mars:

• Time = Distance / Speed
• Time to Mars = \( 54,096,000 \text{ km} / 5,366.67 \text{ km/hour} \approx 10,090 \text{ hours} \)

Now, we convert hours to years:

• \( 10,090 \text{ hours} \div 24 \text{ hours/day} \approx 420.42 \text{ days} \)
• \( 420.42 \text{ days} \div 365 \text{ days/year} \approx 1.15 \text{ years} \)

Based on these calculations, it would take just over 1 year to reach Mars. The closest answer provided from the options is about 1 year.