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.

Question

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)

28.5 cm
28.5 cm

630 cm
630 cm

1.5 cm
1.5 cm

570 cm
570 cm

Answer 1

To determine the maximum possible distance between Mars and Neptune in the scale model, we need to first convert their distances from the sun into centimeters using the given scale of 1 AU = 20 cm.

1. Distance of Mars from the Sun:

   • Mars is 1.5 AU away, which is: $$1.5,\text{AU}\times 20,\text{cm/AU}=30,\text{cm}$$

2. Distance of Neptune from the Sun:

   • Neptune is 30 AU away, which is: $$30,\text{AU}\times 20,\text{cm/AU}=600,\text{cm}$$

3. Maximum Distance Between Mars and Neptune:

   • To find the maximum distance between them when they are on opposite sides of the sun, we simply add their distances from the sun: $$\text{Distance}=\text{Distance from Sun to Mars}+\text{Distance from Sun to Neptune}=30,\text{cm}+600,\text{cm}=630,\text{cm}$$

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

So the answer is: 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)
Responses

about 22.5 years
about 22.5 years

about 1 year
about 1 year

about 2.5 years
about 2.5 years

about 7.5 years

Answer 3

To determine how long it would take the spaceship to reach Mars, we first need to calculate the distance to Mars using the information given:

1. Distance to the Moon: 386,400 km.

2. Distance to Mars: At its closest, Mars is about 140 times farther away than the moon. Thus, the distance to Mars is: $$140\times 386,400,\text{km}=54,096,000,\text{km}.$$

3. Travel Time to the Moon: The spaceship takes 3 days to travel 386,400 km. We can calculate its speed: $$\text{Speed}=\frac{\text{Distance}}{\text{Time}}=\frac{386,400,\text{km}}{3,\text{days}}\approx 128,800,\text{km/day}.$$

4. Travel Time to Mars: Using the calculated speed, we can find out how long it would take to travel to Mars (54,096,000 km): $$\text{Time}=\frac{\text{Distance}}{\text{Speed}}=\frac{54,096,000,\text{km}}{128,800,\text{km/day}}\approx 420,\text{days}.$$

5. Convert days into years: $$420,\text{days}\approx \frac{420}{365}\approx 1.15,\text{years}.$$

Based on this calculation, it would take the spaceship about 1 year to reach Mars.

So the answer is:
about 1 year.

Answer 4

Use the diagram to answer the question.

An illustration shows the sun and the eight planets. The planets are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune.

What is the main problem with this model if it were going to be used to study the dimensions of the solar system?

(1 point)
Responses

The planets are represented in different sizes.
The planets are represented in different sizes.

The planets are shown as having different shapes.
The planets are shown as having different shapes.

The planets are depicted in different colors.
The planets are depicted in different colors.

The planets are placed at the same distance from each other.
The planets are placed at the same distance from each other.
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Answer 5

The main problem with the model of the solar system, if it depicts the planets placed at the same distance from each other, is that this does not accurately represent the actual distances and scale of the solar system. The vast distances between the planets and the sun in real life cannot be represented properly if all planets are shown uniformly spaced.

Therefore, the correct answer is:

The planets are placed at the same distance from each other.

Answer 6

Why do astronomers use astronomical units (AU) instead of kilometers (km)?(1 point)
Responses

Large distances are easier to express in AU than in km.
Large distances are easier to express in AU than in km.

AU is used for spacing, while km is used for length.
AU is used for spacing, while km is used for length.

There are no km in outer space, only AU.
There are no km in outer space, only AU.

AU is used in astronomy, while km is used in physics.

Answer 7

Astronomers use astronomical units (AU) instead of kilometers (km) primarily because the distances within our solar system are extremely large, making it cumbersome to express these distances in kilometers. One AU represents the average distance from the Earth to the Sun, which is about 149.6 million kilometers. Using AU simplifies calculations and makes it easier to communicate and understand distances in space.

Therefore, the correct answer is:

Large distances are easier to express in AU than in km.