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 22.5 years
about 22.5 years

about 1 year
about 1 year

about 2.5 years
about 2.5 years

about 7.5 years
about 7.5 years
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1 answer

To solve this problem, first, we need to determine how far Mars is from Earth at its closest approach, using 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

So, the distance to Mars is:

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

Next, we know that the spaceship takes 3 days to reach the Moon. We need to calculate the speed of the spaceship:

  1. Speed of the spaceship to the Moon:

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{386,400 \text{ km}}{3 \text{ days}} \approx 128,800 \text{ km/day} \]

Now we will use this speed to estimate how long it would take to travel to Mars:

  1. Time to reach Mars:

\[ \text{Time} = \frac{\text{Distance to Mars}}{\text{Speed}} = \frac{54,096,000 \text{ km}}{128,800 \text{ km/day}} \approx 420 \text{ days} \]

Now we convert days to years:

\[ \text{Years} \approx \frac{420 \text{ days}}{365 \text{ days/year}} \approx 1.15 \text{ years} \]

The closest option provided is "about 1 year."

Thus, the best answer is about 1 year.