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 22.5 years about 22.5 years about 7.5 years about 7.5 years about 2.5 years about 2.5 years about 1 year about 1 year
To calculate the approximate time it would take the spaceship to reach Mars, we can use the distance ratio between Mars and the moon.
Given that Mars is about 140 times farther away from Earth than the moon, we can set up the following proportion:
386,400 km (moon distance) : x (Mars distance) = 1 : 140
To find the value of x (Mars distance), we cross multiply:
386,400 km * 140 = x * 1
54,096,000 km = x
Therefore, Mars is approximately 54,096,000 km away from Earth.
Now, let's use the given information that the spaceship took 3 days to reach the moon, which is approximately 386,400 km away. We can set up another proportion to find out how long it would take to reach Mars:
386,400 km (moon distance) : t (time taken to reach Mars) = 1 : 54,096,000 km (Mars distance)
To find the value of t (time taken to reach Mars), we cross multiply:
386,400 km * 54,096,000 km = t * 1
20,933,990,400,000 km = t
Therefore, it would take approximately 20,933,990,400,000 km or 20.9 trillion km to travel from Earth to Mars. Since we are assuming a constant speed, we cannot determine the exact time it would take the spaceship to travel this distance. However, based on the given options, the closest approximation is about 22.5 years.
To calculate the time it would take for the spaceship to reach Mars, we need to determine the distance between Earth and Mars. We know that Mars is about 140 times farther away from Earth than the moon.
The distance from Earth to the moon is approximately 386,400 km. Multiplying this distance by 140 gives us the approximate distance from Earth to Mars:
386,400 km * 140 = 54,096,000 km
Now, we need to determine the speed at which the spaceship can travel. Let's assume that the spaceship can maintain a constant speed and that it travels at the same speed as it did when reaching the moon.
Since the spaceship took 3 days to reach the moon, we can calculate its speed by dividing the distance traveled (386,400 km) by the travel time (3 days):
386,400 km / 3 days = 128,800 km/day
Now, using the calculated distance from Earth to Mars (54,096,000 km) and the spaceship's speed (128,800 km/day), we can find the time it would take to reach Mars:
54,096,000 km / 128,800 km/day = 419.98 days
Rounding this value to the nearest whole number, it would take approximately 420 days for the same spaceship to reach Mars.
Therefore, the correct response is "about 1 year".
To find out how long it would take for the spaceship to reach Mars, we can use the information given.
We know that the moon is about 386,400 km from Earth, and Mars is 140 times farther away from Earth than the moon.
So, to find the distance to Mars, we can multiply the distance to the moon (386,400 km) by the multiplier of 140:
Distance to Mars = 386,400 km * 140 = 54,096,000 km
Now, we need to determine how long it would take for the spaceship to travel this distance.
We are given that the spaceship reaches the moon in 3 days. Let's assume it travels at a constant speed.
Distance (386,400 km) / Time (3 days) = Speed
Speed = 386,400 km / 3 days = 128,800 km/day
Using this speed, we can find the time it would take to reach Mars by dividing the distance to Mars by the speed:
Time to reach Mars = Distance to Mars / Speed
Time to reach Mars = 54,096,000 km / 128,800 km/day
Calculating this value gives us approximately 419.93 days.
Therefore, the spaceship would take about 419.93 days, or roughly 1.15 years, to reach Mars.