Solar System Distances Quick Check
2 of 42 of 4 Items
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?(1 point)
Responses
about 2.5 years
about 2.5 years
about 22.5 years
about 22.5 years
about 1 year
about 1 year
about 7.5 years
The correct answer is:
about 7.5 years
To calculate the approximate time it would take for the spaceship to reach Mars, we need to consider that Mars is about 140 times farther away from Earth than the Moon.
Given that the spaceship reaches the Moon in 3 days, we can set up a proportion to find the time it would take to reach Mars:
Moon distance / Moon travel time = Mars distance / Mars travel time
Substituting the given values:
386,400 km / 3 days = Mars distance / Mars travel time
To find the Mars travel time, we can cross multiply and solve for it:
Mars travel time = (386,400 km * Mars distance) / (3 days)
Since Mars is about 140 times farther away from Earth than the Moon, we can substitute Mars distance with 140 * Moon distance:
Mars travel time = (386,400 km * (140 * Moon distance)) / (3 days)
Simplifying the expression, we get:
Mars travel time = (386,400 km * 140 * 386,400 km) / (3 days * 3 days)
Calculating this expression, we find that the spaceship would take approximately 7.5 years to reach Mars.
Therefore, the correct response is: about 7.5 years.