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 22.5 years
about 22.5 years

about 2.5 years
about 2.5 years

about 7.5 years

Answer 1

To determine how long it would take the spaceship to reach Mars, we first need to calculate the distance to Mars based on the information given.

1. Distance to the Moon: 386,400 km
2. Closest distance to Mars: \( 140 \times 386,400 \) km

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

Next, we find the time it takes to reach the moon, which is given as 3 days. We need to find the speed of the spaceship:

1. Speed of the spaceship:

   • Distance to the Moon: 386,400 km
   • Time to reach the Moon: 3 days = 3 × 24 hours = 72 hours

   So, the speed \( v \) is: \[ v = \frac{\text{Distance}}{\text{Time}} = \frac{386,400 \text{ km}}{72 \text{ hours}} \approx 5,366.67 \text{ km/h} \]

2. Time to reach Mars: Now we can calculate the time it would take to reach Mars at the same speed.

   The time \( t \) is given by: \[ t = \frac{\text{Distance}}{\text{Speed}} = \frac{54,096,000 \text{ km}}{5,366.67 \text{ km/h}} \] Calculating \( t \): \[ t \approx 10,096.2 \text{ hours} \]

Now converting hours to years (1 year ≈ 8,760 hours): \[ t \approx \frac{10,096.2 \text{ hours}}{8,760 \text{ hours/year}} \approx 1.15 \text{ years} \]

So, it would take about 1 year to reach Mars with that spaceship.

Thus, the correct response is:

about 1 year.