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

Answer 1

To determine how long it would take the spaceship to reach Mars, we first need to find the distance to Mars.

1. Distance to the Moon: 386,400 km
2. Closest distance from Earth to Mars: about 140 times the distance to the Moon. \[ \text{Distance to Mars} = 140 \times 386,400 \text{ km} = 54,096,000 \text{ km} \]

Next, we find the speed of the spaceship based on its travel time to the Moon.

3. Time taken to reach the Moon: 3 days = 3 × 24 hours = 72 hours
4. Speed of the spaceship: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{386,400 \text{ km}}{72 \text{ hours}} \approx 5,366.67 \text{ km/hour} \]

Now, we can find out how long it would take to reach Mars at that speed.

5. Time taken to reach Mars: \[ \text{Time} = \frac{\text{Distance to Mars}}{\text{Speed}} = \frac{54,096,000 \text{ km}}{5,366.67 \text{ km/hour}} \approx 10,080 \text{ hours} \]
6. Convert hours to days: \[ 10,080 \text{ hours} = \frac{10,080}{24} \text{ days} \approx 420 \text{ days} \]
7. Convert days to years: \[ \text{Time in years} = \frac{420}{365} \approx 1.15 \text{ years} \]

Therefore, the spaceship would take about 1 year to reach Mars, based on the initial assumptions and calculations.

The correct response is: about 1 year.