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

1 answer

To estimate the travel time to Mars based on the information provided, we can use the distances to both celestial bodies.

  1. The distance to the moon is approximately 386,400 km.

  2. Mars is about 140 times farther away from Earth than the moon, so the distance to Mars at its closest is:

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

  3. If we assume the spaceship takes 3 days (72 hours) to travel the 386,400 km to the moon, we can calculate its speed:

    \[ \text{Speed} = \frac{386,400 \text{ km}}{72 \text{ hours}} \approx 5,366.67 \text{ km/hour} \]

  4. Now, to find out how long it would take to cover the distance to Mars at the same speed:

    \[ \text{Time} = \frac{\text{Distance to Mars}}{\text{Speed}} = \frac{54,096,000 \text{ km}}{5,366.67 \text{ km/hour}} \approx 10,100 \text{ hours} \]

  5. To convert hours into years:

    \[ \text{Years} = \frac{10,100 \text{ hours}}{24 \text{ hours/day} \times 365 \text{ days/year}} \approx 1.15 \text{ years} \]

Therefore, the closest approximation for how long it would take that spaceship to reach Mars is about 1 year.