by Anthony Barreiro » Thu Jan 31, 2013 12:09 am
MargaritaMc wrote:Anthony Barreiro wrote:<<
From two kilometers distant, the people would have tiny angular dimensions, accounting for how much smaller they look than the half-degree wide Moon.
Can you explain, please, Anthony?
Many thanks
Margarita
I'll try.
The Moon is about 3500 kilometers in diameter and about 385,000 kilometers distant from the Earth. From the surface of the Earth, the Moon appears about half a degree wide, or thirty arcminutes wide. Your pinkie finger is about a centimeter wide. If you hold your pinkie finger out at arms length it's about a degree wide, twice as wide as the Moon, and will easily cover the Moon.
From two kilometers away, a 1.75 meter tall human body looks tiny, about 3 arcminutes tall, or about one tenth as tall as the width of the Moon. In this video Mark Gee used a telescope to magnify both the Moon and the people, so the Moon looks huge and we see a lot of detail on the surface of the Moon, and the people are magnified enough to show detail in their silhouettes. No matter how much you magnify the Moon and the people, with the people two kilometers away and the Moon 385,000 kilometers away, the Moon appears 10 times as big as the people. If you were looking through a telescope one kilometer away from the people, the Moon would look 5 times as big as the people. From four kilometers away, the Moon would look 20 times as big as the people. The important principle is that the angular size of an object shrinks by half when the distance to the object is doubled.
By the way, the relationship between diameter, distance, and angular size is why we experience total solar eclipses here on Earth. The diameter of the Sun is 400 times greater than the diameter of the Moon. The Sun is also 400 times farther away from the Earth than the Moon is. Voila, both the Sun and the Moon appear about one-half degree wide, and when the Moon passes exactly in front of the Sun (and when she is close to the Earth in her elliptical orbit), she completely covers the Sun, causing an eclipse. The Earth is the only planet in our solar system where this happy coincidence occurs.
[quote="MargaritaMc"][quote="Anthony Barreiro"]<<
From two kilometers distant, the people would have tiny angular dimensions, accounting for how much smaller they look than the half-degree wide Moon.[/quote]
Can you explain, please, Anthony?
Many thanks :)
Margarita[/quote]
I'll try.
The Moon is about 3500 kilometers in diameter and about 385,000 kilometers distant from the Earth. From the surface of the Earth, the Moon appears about half a degree wide, or thirty arcminutes wide. Your pinkie finger is about a centimeter wide. If you hold your pinkie finger out at arms length it's about a degree wide, twice as wide as the Moon, and will easily cover the Moon.
From two kilometers away, a 1.75 meter tall human body looks tiny, about 3 arcminutes tall, or about one tenth as tall as the width of the Moon. In this video Mark Gee used a telescope to magnify both the Moon and the people, so the Moon looks huge and we see a lot of detail on the surface of the Moon, and the people are magnified enough to show detail in their silhouettes. No matter how much you magnify the Moon and the people, with the people two kilometers away and the Moon 385,000 kilometers away, the Moon appears 10 times as big as the people. If you were looking through a telescope one kilometer away from the people, the Moon would look 5 times as big as the people. From four kilometers away, the Moon would look 20 times as big as the people. The important principle is that the angular size of an object shrinks by half when the distance to the object is doubled.
By the way, the relationship between diameter, distance, and angular size is why we experience total solar eclipses here on Earth. The diameter of the Sun is 400 times greater than the diameter of the Moon. The Sun is also 400 times farther away from the Earth than the Moon is. Voila, both the Sun and the Moon appear about one-half degree wide, and when the Moon passes exactly in front of the Sun (and when she is close to the Earth in her elliptical orbit), she completely covers the Sun, causing an eclipse. The Earth is the only planet in our solar system where this happy coincidence occurs.