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?

about 1 year
about 1 year

about 7.5 years
about 7.5 years

about 2.5 years
about 2.5 years

about 22.5 years

Answer 1

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

Given that the distance to the Moon is approximately 386,400 km and Mars is about 140 times farther away, we can calculate the distance to Mars as follows:

Distance to Mars = Distance to Moon × 140
Distance to Mars = 386,400 km × 140 = 54,096,000 km

Next, we need to find the speed of the spaceship based on its journey to the Moon. If the spaceship reaches the Moon in 3 days, we can compute its speed:

Speed = Distance / Time
Time to reach the Moon in hours = 3 days × 24 hours/day = 72 hours

Speed = 386,400 km / 72 hours ≈ 5,366.67 km/hour

Now we can use this speed to calculate the time it would take to reach Mars:

Time = Distance / Speed
Time to reach Mars = 54,096,000 km / 5,366.67 km/hour ≈ 10,085.6 hours

To convert hours into years, we can divide by the number of hours in a year:

1 year = 365 days × 24 hours/day = 8,760 hours
Time to reach Mars in years = 10,085.6 hours / 8,760 hours/year ≈ 1.15 years

Therefore, the approximate time it would take the spaceship to reach Mars would be about **1 year**.