Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 4: Problem 1

If the sun were the size of a basketball, how large would Earth be, and how far away? How large would the moon be, and how far from Earth, at this scale?

Short Answer

Expert verified
Answer: At this scale, the Earth would be 0.002 cm in diameter, the Moon would be 0.0006 cm in diameter, the distance between the Sun and Earth would be 25.8 cm, and the distance between Earth and Moon would be 0.007 cm.

Step by step solution

01

Gather necessary information

We need to know the actual diameters of the Sun, Earth, and Moon, as well as the actual distances between the Sun and Earth, and the Earth and Moon. Here are the numbers we will use (rounded for simplicity): 1. Sun diameter: 1,391,000 km 2. Earth diameter: 12,742 km 3. Moon diameter: 3,474 km 4. Distance between Sun and Earth: 149,600,000 km 5. Distance between Earth and Moon: 384,400 km Basketball diameter: 24 cm
02

Calculate the scaling ratio

We will find the ratio between the Sun's diameter and the basketball's diameter. This ratio will be used to scale down the sizes and distances. Scaling ratio = (Basketball diameter) / (Sun diameter) Scaling ratio = 24 cm / 1,391,000 km = 24 / (1,391,000 * 100,000) = 1 / 5,795,833,333
03

Scale down Earth's size

Now, we will multiply Earth's diameter by the scaling ratio to find the size of Earth at this scale. Scaled Earth diameter = Earth diameter × Scaling ratio Scaled Earth diameter = 12,742 km × (1 / 5,795,833,333) = 0.002 cm
04

Scale down the Moon's size

Next, we will multiply the Moon's diameter by the scaling ratio to find the size of the Moon at this scale. Scaled Moon diameter = Moon diameter × Scaling ratio Scaled Moon diameter = 3,474 km × (1 / 5,795,833,333) = 0.0006 cm
05

Scale down the distance between Sun and Earth

Now, we will multiply the distance between Sun and Earth by the scaling ratio to find the scaled distance at this scale. Scaled Sun-Earth distance = Sun-Earth distance × Scaling ratio Scaled Sun-Earth distance = 149,600,000 km × (1 / 5,795,833,333) = 25.8 cm
06

Scale down the distance between Earth and Moon

Lastly, we will multiply the distance between Earth and Moon by the scaling ratio to find the scaled distance at this scale. Scaled Earth-Moon distance = Earth-Moon distance × Scaling ratio Scaled Earth-Moon distance = 384,400 km × (1 / 5,795,833,333) = 0.007 cm So, at this scale: 1. Earth would be 0.002 cm in diameter. 2. The Moon would be 0.0006 cm in diameter. 3. The distance between the Sun and Earth would be 25.8 cm. 4. The distance between Earth and Moon would be 0.007 cm.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

List at least three space achievements that impress you personally, even if they do not bear directly on colonization aims.

Highway 6563 in New Mexico has signs along a roughly \(30 \mathrm{~km}\) stretch of road corresponding to the solar system scale from the Sun to Neptune. On this scale, how large would Earth, Sun, and Jupiter be, in diameter? Express in convenient units appropriate to the scale.

Prior to exposure to this material, what would you honestly have said in response to: How far have humans been from the planet in the last 45 years; a) \(600 \mathrm{~km}\) (about \(\frac{1}{10}\) Earth radius; low earth orbit) b) \(6,000 \mathrm{~km}\) (roughly Earth radius) c) \(36,000 \mathrm{~km}\) (about \(6 R_{\oplus} ;\) around geosynchronous orbit) d) \(385,000 \mathrm{~km}\) (approximate distance to the moon) e) beyond the distance to the moon Explain what led you to think so (whether correct or not).

For some perspective, imagine you were able to drive your car up a ramp to an altitude characteristic of low-earth orbit (about \(320 \mathrm{~km}\), or 200 miles). It takes about \(5 \times 10^{10} \mathrm{~J}\) of energy \(^{33}\) to win the fight against gravity. Meanwhile, each gallon of gasoline can do about \(25 \times 10^{6} \mathrm{~J}\) of useful work. How many gallons would it take to climb to orbital height in a car? Roughly how many miles per gallon is this (just counting vertical miles)?
See all solutions

Recommended explanations on Environmental Science Textbooks

Ecological Conservation

Read Explanation

Environmental Research

Read Explanation

Energy Resources

Read Explanation

Living Environment

Read Explanation

Sustainability

Read Explanation

Biological Resources

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free