Calculating distance using parallax is a useful skill amateur astronomers can use to enhance own stargazing (and practise a bit of maths!). It can only be used with very close stars, and the accuracy is dependent on the resolution of your equipment. All it takes is three simple but year-long steps!
What Is Parallax?
As you travel, the objects closer to you move faster than objects further away. This parallax, and how quickly the objects move are determined by how far away they are. The Earth’s motion around the sun causes a larger movement of very close stars relative to distant ones.
Let’s Use It!
STEP 1: To find the distance of a nearby star using parallax, you need to watch the star’s movement over the year relative to nearby distant stars. I recommend taking pictures of the target star with one or more background stars.
Bear in mind, you will need a scale to work with when taking pictures. This can be done by knowing how much sky your camera is capturing (field of view). Alternatively, if there’s a few background stars, you can use a sky chart to find their distance in degrees/arcseconds, and calibrate that for your final measurements.
The target star will move in an elliptical shape (circle, oval, or line). The distant stars will stay pretty much put.
STEP 2: You can find the elliptical path of the star by comparing all your images, either by hand or by using software. Measure the semi-major axis (distance from center to furthest point). This is where your scale/field of view comes into play, so you can calibrate your measurement from your ruler reading to actual arcseconds.
STEP 3: All that’s left is to use this handy formula:
D = 1/θ
D = distance (in parsecs)
θ = semi-major axis (in arcseconds)
So, if a star had a measured semi-major axis of 0.005 degrees, we’d first convert it to arcseconds (18 arcseconds) and then sub it into the formula to get 0.06 parsecs.
That was a short intro to parallax. Hopefully you’ll be able to use it in your stargazing at least once, as it’s really rewarding to get a measurement. That’s it for this week. I’ll be back with some black hole basics!
Parallax is an interesting technique, which I didn’t think that I could use with my own telescope! You mentioned that it is for close stars, so what would we use for far away stuff?
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Parallax is part of something called the Distance ladder, where we calibrate our results to use with a different technique. After parallax, astronomers often use main sequence fitting, which we’ll cover next year!
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