Solar System Distances Quick Check

2 of 42 of 4 Items

Question
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 2.5 years
about 2.5 years

about 7.5 years
about 7.5 years

about 22.5 years

1 answer

To find out how long it would take the spaceship to reach Mars, we can use the information provided.

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

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

  1. Time to reach the Moon: 3 days.

Next, we can calculate the speed of the spaceship. We can convert the time in days to hours (3 days = 72 hours) and find the speed: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{386,400 \text{ km}}{72 \text{ hours}} \approx 5,366.67 \text{ km/h} \]

Now, we can calculate the time to reach Mars: \[ \text{Time to reach Mars} = \frac{\text{Distance to Mars}}{\text{Speed}} = \frac{54,096,000 \text{ km}}{5,366.67 \text{ km/h}} \approx 10,100 \text{ hours} \]

Next, convert hours to years (there are about 8,760 hours in a year): \[ \text{Time in years} = \frac{10,100 \text{ hours}}{8,760 \text{ hours/year}} \approx 1.15 \text{ years} \]

Based on that approximation, the closest response is about 1 year.