Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Problem 24

How did Aristarchus try to estimate the diameters of the Sun and Moon?

Short Answer

Expert verified
Aristarchus attempted to estimate the diameters of the Sun and the Moon by observing lunar eclipses and creating geometric relations based on the shadows cast during these eclipses. Based on the geometry and his observations, he deduced that the diameter of the Earth was 3 times that of the Moon, and that the diameter of the Sun was even larger.

Step by step solution

01

Identify Aristarchus's Method

Aristarchus of Samos is known for his theories on the relative sizes of the sun, moon and Earth. His method relies on the observation of lunar eclipses, and how these eclipses are related to the relative positions of the Sun, Earth, and Moon.
02

Explain Aristarchus's Observations

During a lunar eclipse, the Earth is exactly between the Sun and the Moon. Aristarchus observed that the Moon was in the Earth's shadow, and he reasoned that the Sun’s diameter was larger than the Earth’s because the shadow cast during an eclipse could fully cover the Moon.
03

Describe Aristarchus's Mathematical Deductions

Aristarchus figured that the diameter of the Earth is 3 times that of the Moon due to the shadows cast during a lunar eclipse. Assuming the Earth's orbit around the Sun as a circle, he set up a geometric relation that enabled him to solve for the relative diameters of the Sun and the Moon using angular measurements.

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

What is the line of nodes? Why is it important to the subject of eclipses?

How did Aristarchus try to estimate the distance from the Earth to the Sun and Moon?

You are watching a lunar eclipse from some place on the Earth's night side. Will you see the Moon enter the Earth's shadow from the east or from the west? Explain your reasoning.

The plane of the Moon's orbit is inclined at a \(5^{\circ}\) angle from the ecliptic, and the ecliptic is inclined at a \(231 / 2^{\circ}\) angle from the celestial equator. Could the Moon ever appear at your zenith if you lived at (a) the equator; (b) the south pole? Explain your answers.

In his 1885 novel King Solomon's Mines, H. Rider Haggard described a total solar eclipse that was seen in both South Africa and in the British Isles. Is such an eclipse possible? Why or why not?
See all solutions

Recommended explanations on Physics Textbooks

Classical Mechanics

Read Explanation

Turning Points in Physics

Read Explanation

Linear Momentum

Read Explanation

Torque and Rotational Motion

Read Explanation

Kinematics Physics

Read Explanation

Fields in Physics

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