Question

Use this paragraph: In a scale model of the solar system, the sun is placed at the center and the planets are shown orbiting in circles around it. Mars is 1.5 AU away from the sun and in the model, it appears at 30 cm from it which means that 1 AU = 20 cm. Likewise, Neptune is 30 AU away from the sun. What is the maximum possible distance that can be drawn between Mars and Neptune in the scale model? Hint: Two planets are as far apart as possible when they are on directly opposite sides of the sun from each other. Draw a picture with the planets as far apart as possible.

(1 point)
O 570 cm
O 630 cm
O 28.5 cm
O 15 cm

Answer 1

[AI-generated answer — Bot GPT 3.5]

In the scale model, 1 AU is equal to 20 cm. Therefore, the distance between Mars and the Sun in the model is 1.5 AU x 20 cm/AU = 30 cm.

To determine the maximum possible distance between Mars and Neptune in the scale model, we need to find the distance between Neptune and the Sun in the model. Since Neptune is 30 AU away from the Sun, the distance between Neptune and the Sun in the model is 30 AU x 20 cm/AU = 600 cm.

To find the maximum possible distance between Mars and Neptune in the model, we add the distances between each planet and the Sun:

30 cm (distance between Mars and the Sun) + 600 cm (distance between Neptune and the Sun) = 630 cm.

Therefore, the maximum possible distance that can be drawn between Mars and Neptune in the scale model is 630 cm.

The correct answer is O 630 cm.

Answer 2

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)

O about 1 year
O about 22.5 years
O about 2.5 years
O about 7.5 years

Answer 3

[AI-generated answer — Bot GPT 3.5]

If the moon is 386,400 km away from Earth and the spaceship takes 3 days to reach it, we can calculate the spaceship's speed as follows:

Speed = Distance / Time
Speed = 386,400 km / 3 days

To calculate the speed in km/day, we divide the distance by the time:
Speed = 128,800 km/day.

Since Mars is about 140 times farther away from Earth than the moon, we can find the distance to Mars by multiplying the moon's distance by 140:
Distance to Mars = 386,400 km * 140

Now, we can calculate the time it would take for the spaceship to reach Mars using the calculated speed:
Time = Distance / Speed
Time = (386,400 km * 140) / (128,800 km/day)

Simplifying the equation gives us:
Time = 386,400,000 km / 128,800 km/day

Calculating the time gives us:
Time ≈ 3000 days

Converting the time to years, we divide by 365 since there are approximately 365 days in a year:
Time ≈ 3000 days / 365 days/year

Rounding the result to the nearest whole number, we get:
Time ≈ 8.21 years ≈ 8 years.

Therefore, the spaceship would take about 8 years to reach Mars.

The closest answer choice is O about 7.5 years, which is the most appropriate approximation.