Questions: Why did Aristarchus choose the time of a half Moon to make his measurements for calculating the Earth -Sun distance? The Earth, Moon, and Sun formed a straight line at that time The Earth, Moon, and Sun formed a right triangle at that time The Earth, Moon, and Sun formed an acute triangle at that time. The Earth, Moon, and Sun formed an obtuse triangle at that time.

Why did Aristarchus choose the time of a half Moon to make his measurements for calculating the Earth -Sun distance?
The Earth, Moon, and Sun formed a straight line at that time
The Earth, Moon, and Sun formed a right triangle at that time
The Earth, Moon, and Sun formed an acute triangle at that time.
The Earth, Moon, and Sun formed an obtuse triangle at that time.

Transcript text: Why did Aristarchus choose the time of a half Moon to make his measurements for calculating the Earth -Sun distance? The Earth, Moon, and Sun formed a straight line at that time The Earth, Moon, and Sun formed a right triangle at that time The Earth, Moon, and Sun formed an acute triangle at that time. The Earth, Moon, and Sun formed an obtuse triangle at that time.

Solution

Solution Steps

Step 1: Understanding the Context

Aristarchus of Samos was an ancient Greek astronomer who attempted to determine the distance from the Earth to the Sun. He used the geometry of the Earth-Moon-Sun system during specific lunar phases to make his calculations.

Step 2: Identifying the Key Concept

Aristarchus chose the time of a half Moon (first or third quarter) because, at this time, the Earth, Moon, and Sun form a specific geometric configuration. This configuration is crucial for making accurate measurements.

Step 3: Analyzing the Geometric Configuration

At the time of a half Moon, the angle between the Earth, Moon, and Sun is 90 degrees. This means that the Earth, Moon, and Sun form a right triangle, with the right angle at the Moon.