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)
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• about 7.5 years
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• about 1 year
• about 22.5 years
• about 2.5 years
If the spaceship takes 3 days to reach the moon, which is approximately 386,400 km away, then its average speed is about 128,800 km per day (386,400 km / 3 days = 128,800 km/day).
Mars is about 140 times farther away from Earth than the moon (386,400 km * 140 = 54,096,000 km).
Using the spaceship's average speed of 128,800 km/day, it would take approximately 420 days to reach Mars (54,096,000 km / 128,800 km/day = 420 days).
Therefore, it would take about 1 year for the spaceship to reach Mars.
To determine how long it would take the spaceship to reach Mars, we can use the given information that Mars is about 140 times farther away from Earth than the moon.
Given that it takes 3 days to reach the moon, we can calculate the approximate time it would take to reach Mars by multiplying the time it takes to reach the moon by the distance ratio between Earth-Moon and Earth-Mars.
So the calculation would be:
Time to reach Mars = Time to reach the moon * Distance ratio
Time to reach Mars = 3 days * 140
Time to reach Mars ≈ 420 days
Therefore, the spaceship would take about 1 year (approximately 420 days) to reach Mars.
The correct answer is:
about 1 year.
To determine how long it would take the spaceship to reach Mars, we can use the information given about the distance between Earth and the moon, as well as the distance between Earth and Mars.
We are told that the moon is about 386,400 km away from Earth and that Mars, at its closest, is about 140 times farther away from us than the moon.
So, the distance between Earth and Mars can be calculated as follows:
Distance to Mars = Distance to moon x 140 = 386,400 km x 140 = 54,096,000 km
Now, we need to figure out how long it would take to travel this distance. We are given that the spaceship reaches the moon in 3 days. To estimate the time it would take to reach Mars, we can set up a proportion:
3 days (to reach the moon) is to 386,400 km (to the moon) as X days (to reach Mars) is to 54,096,000 km (to Mars).
Using cross multiplication, we can solve for X:
X = (3 days) * (54,096,000 km) / (386,400 km)
X ≈ 421.17 days
Rounding to the nearest whole number, we can say that it would take about 421 days for the spaceship to reach Mars.
Therefore, the correct answer is:
• About 1 year.