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)
about 7.5 years
about 1 year
about 2.5 years
about 22.5 years
To find the estimated time it would take for the spaceship to reach Mars, we can use the proportion based on the distance comparison between the moon and Mars:
Moon distance: 386,400 km
Mars distance: 140 times farther than the moon
So, Mars distance = 386,400 km * 140 = 54,096,000 km
Now, we can set up a proportion to find the time it would take to reach Mars:
Moon travel time: 3 days
Mars travel time: x days
Moon distance: 386,400 km
Mars distance: 54,096,000 km
The proportion is:
3 days / 386,400 km = x days / 54,096,000 km
Cross-multiplying and solving for x:
386,400 km * x days = 3 days * 54,096,000 km
386,400x = 162,288,000 days
x ≈ 162,288,000 days / 386,400
x ≈ 420.51 days
Therefore, it would take approximately 420.51 days (or about 1 year and 55.5 days) for the same spaceship to reach Mars. Therefore, the closest answer choice is about 1 year.
To find out how long it would take for the same spaceship to reach Mars, we need to consider that Mars is about 140 times farther away from Earth than the moon.
If it takes 3 days to reach the moon, which is approximately 386,400 km away, we can calculate the distance to Mars by multiplying this distance by 140.
386,400 km x 140 = 54,096,000 km
Now, assuming the spaceship maintains the same speed as it did to reach the moon, we can calculate the time it would take to reach Mars by dividing the distance to Mars by the average speed of the spaceship.
Let's assume the average speed of the spaceship remains constant at approximately 29,200 km/h.
54,096,000 km ÷ 29,200 km/h = 1,853.56 hours
Finally, we convert this time to years by dividing it by the number of hours in a year, which is approximately 8,760 hours.
1,853.56 hours ÷ 8,760 hours/year ≈ 0.21 years
So, the spaceship would take about 0.21 years or approximately 2.5 months to reach Mars, given this simple model of the solar system.
Therefore, the correct answer is: about 2.5 years.