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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.

Responses

1.5 cm
1.5 cm

630 cm
630 cm

28.5 cm
28.5 cm

570 cm

7 answers

To find the maximum possible distance between Mars and Neptune in the scale model, we first need to determine the distances from the Sun to each planet in the scale model based on the given information.

  • Distance from the Sun to Mars: It is given that Mars is 1.5 AU away from the sun. Since 1 AU = 20 cm, the distance from the Sun to Mars in the model is: \[ 1.5 , \text{AU} \times 20 , \text{cm/AU} = 30 , \text{cm} \]

  • Distance from the Sun to Neptune: Neptune is 30 AU away from the sun. Using the same scale: \[ 30 , \text{AU} \times 20 , \text{cm/AU} = 600 , \text{cm} \]

To find the maximum distance between Mars and Neptune, we need to consider that this distance occurs when the two planets are on opposite sides of the sun. Therefore, the maximum distance is the sum of the distances from both planets to the sun:

\[ \text{Maximum distance} = \text{Distance to Mars} + \text{Distance to Neptune} \] \[ \text{Maximum distance} = 30 , \text{cm} + 600 , \text{cm} = 630 , \text{cm} \]

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

The correct response is: 630 cm

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 7.5 years
about 7.5 years

about 22.5 years
about 22.5 years

about 1 year
about 1 year

about 2.5 years

To determine how long it would take the spaceship to reach Mars, we first need to understand the distance to Mars relative to the distance to the Moon.

  1. Distance to the Moon: 386,400 km
  2. Mars is 140 times farther than the Moon: \[ \text{Distance to Mars} = 140 \times \text{Distance to Moon} = 140 \times 386,400 , \text{km} = 54,096,000 , \text{km} \]

Next, we find out how long it takes the spaceship to travel 386,400 km (the distance to the Moon) in 3 days. We can calculate the speed of the spaceship:

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{386,400 , \text{km}}{3 , \text{days}} = 128,800 , \text{km/day} \]

Now, we can find the time it would take to reach Mars at this speed:

\[ \text{Time to reach Mars} = \frac{\text{Distance to Mars}}{\text{Speed}} = \frac{54,096,000 , \text{km}}{128,800 , \text{km/day}} \approx 420 , \text{days} \]

To convert days into years:

\[ \text{Time in years} = \frac{420 , \text{days}}{365} \approx 1.15 , \text{years} \]

Since 1.15 years is just over 1 year, we can reasonably round this to about 1 year.

Thus, the answer is: about 1 year.

Use the diagram to answer the question.

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

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

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

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

The main problem with the model if it were going to be used to study the dimensions of the solar system is:

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

In reality, the distances between the planets vary significantly and cannot be accurately represented if they are all shown at the same distance from each other. This misrepresentation would lead to incorrect conclusions about the layout and scale of the solar system.

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

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.

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 in astronomy, while km is used in physics.

The correct response is:

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

This is because astronomical distances, such as those between planets and stars, are extremely large, making it more convenient to use astronomical units (where 1 AU is the average distance from the Earth to the Sun, approximately 149.6 million kilometers) instead of dealing with very large numbers in kilometers. Using AU helps to simplify communication and calculations regarding the vast distances in space.