Have you ever wondered how big the moon is, or how far apart the stars are? If you are a stargazer, you might be curious about the size and scale of the objects in the night sky.
But how can you measure them without any fancy equipment?
The answer is simple: use your fingers and hands! All you need is a clear night sky, a good view of the horizon, and some basic knowledge of astronomy.
What are angular distances and why they are important
When we look at the sky, we see a dome of stars that seems to surround us. This is an illusion caused by the fact that we are on a spherical planet and the stars are very far away. To measure the distance between two objects in the sky, we can’t use the usual units of length, such as meters or miles, because they are too small and impractical. Instead, we use angular distances, which are based on the angle that the objects make with our eyes.
Imagine drawing a line from your eye to one object, and another line from your eye to another object. The angle between these two lines is the angular distance between the objects. Angular distances are measured in degrees (°), arc minutes (‘), and arc seconds ("). There are 360 degrees in a circle, 60 arc minutes in a degree, and 60 arc seconds in an arc minute. For example, the angular distance between the two pointers of the Southern Cross is about 6 degrees.
Angular distances are important because they help us understand the size and scale of the objects in the sky. To find out how big an object is from its angular size and distance, we can use a simple formula that comes from trigonometry:
l=d×tan(theta)
where l is the size of the object, d is the distance to the object, and theta is the angular size of the object (in radians, to convert from degrees to radians, you can use this formula: radians = degrees × π / 180°).
This formula works best when the angular size is small.
For example, if we know that the moon has an angular size of 0.5 degrees (or 0.0087 radians) and a distance of about 384,000 km from Earth, we can use the formula to find out how big the moon is:
l=384000×tan(0.0087)
l=3345km
This means that the moon has a diameter of about 3345 km.
How to use your hand as a measuring tool
One of the easiest ways to estimate angular distances in the sky is to use your hand as a measuring tool. All you need to do is hold your hand at arm’s length and close one eye. Then you can use different parts of your hand to measure different angles. Here are some common measurements:
Your clenched fist is about 10 degrees wide.
The width of your little finger is about 1 degree.
The span between your thumb and little finger when stretched out is about 25 degrees.
The span between your index finger and little finger when stretched out is about 15 degrees.
Your three middle fingers are about 5 degrees wide.
Of course, these measurements are approximate and may vary depending on the size of your hand and arm. But they are good enough for most purposes.
How to apply this technique to find and compare objects in the southern sky
Now that you know how to measure angular distances with your hand, you can use this technique to find and compare objects. Here are some examples:
To find the Southern Cross (Crux), you can look for its distinctive shape of four bright stars forming a cross. The Southern Cross spans about 6 degrees from top to bottom, so you can use your little finger and index finger to measure it. The Southern Cross also has two bright stars on either side of it: Alpha Centauri and Beta Centauri. These stars are called the Pointers because they point towards the Southern Cross. The angular distance between Alpha Centauri and Beta Centauri is about 4 degrees, so you can use three fingers to measure it.
To find Canopus, the second brightest star in the night sky after Sirius, you can use your fist as a guide. Canopus is about 40 degrees south of Sirius, which means it is four fists below Sirius when viewed from the horizon. Canopus has an angular diameter of only 0.006 arc minutes, which means it appears as a point of light in the sky. However, it is actually a huge star that is about 71 times larger than our sun. Canopus is in the constellation Carina.
To compare the size of Jupiter and Saturn, you can use your little finger to measure their angular diameter. Jupiter has an angular diameter of about 0.7 degrees, which means it appears to be slightly larger than your little finger at arm’s length. Saturn has an angular diameter of about 0.4 degrees, which means it appears to be slightly smaller than your little finger. However, this does not include the rings of Saturn, which can extend up to 0.8 degrees in the sky.
With this new found knowledge, go forth my young Padawan. Explore the night sky and try your hand (or pinky) at measuring the angular distance of night sky objects.
This skill is a fun and easy way to survey the night sky and appreciate the beauty of our galaxy.
I hope you found it interesting and informative. If you have any questions or feedback, feel free to leave a comment below.
Clear skies!
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