In this project you are going to calculate the diameters of some planets in the

In this project you are going to calculate the diameters of some planets in the

In this project you are going to calculate the diameters of some planets in the same way you calculated the height of a building in the last project. The planets are too far away for you to measure their angular size (what we were calling elevation angle in the last project), so I will supply those very tiny angles and you will apply the arithmetic you used in the last project to calculate the diameters of some planets. What’s the point? For one thing, so you can get a little taste of applying the same methods that astronomers have used for centuries, not just for planet sizes, but for many problems involving size and distance. I recently published a couple of scientific papers in which I used the very same right triangle relationships that you have been using. It comes up all the time in physical science. In a later project you will use these diameters to build a scale model of the Solar System.
Think about your field of view. How many degrees are there all the way around in your field of view? Answer: 360 degrees. Most of you probably knew that.
How much of your field of view is occupied by the width of your little finger held at arm’s length? About 1 degree.
How much of your field of view is occupied by the Sun? 1/2 degree. Moon? 1/2 degree.
From top to bottom, that building you measured in the last project occupied at least ten degrees in your field of view.
How about the planet Mercury? When Mercury is as far away as the Earth–Sun distance, it occupies only 0.00186 degrees in your field of view. That’s a very small angle, but Mercury is VERY far away. The Earth–Sun distance has a special name: the Astronomical Unit. One AU equals 150,000,000 kilometers (km).
Well, hell, if we know the angle Mercury occupies in our field of view, and we know how far away it is, we can use the same formula we used in the last project, to calculate the distance from one side of Mercury to the other. In other words, it’s diameter. Instead of calculating the distance from the ground to the top of a building, we are going to calculate the distance from one side of Mercury to the other.
diameter = tangent (angular diameter) x distance
Diameter of Mercury = tangent (0.00186) x 150,000,000 km = 4869 km
Diameter of Mercury = 0.0000325 x 150,000,000 km
Diameter of Mercury = 4869 km
If you don’t have a calculator with trig functions, buy, borrow or steal one. Or if you don’t want to do that, simply go to Google and type: tangent 0.00186 degrees. Google will return 0.0000325. Tangent of 0.00186 equals 0.0000325. You must type degrees after the number, or you will get the wrong answer.
Below I give you the angular diameters of some planets, as measured from the Earth, and their distances from the Earth. I want you to calculate their diameters using the formula below (used in the above example):
diameter = tangent (angular diameter) x distance
Distance at time of measurement Angular Diameter at time of measurement Diameter
Mercury 150,000,000 km 0.00186 degrees 4869 km
Venus 150,000,000 km 0.00462 degrees ?
Mars 150,000,000 km 0.00259 degrees ?
Jupiter 750,000,000 km 0.01090 degrees ?
Saturn 1,500,000,000 km 0.00460 degrees ?
Uranus 2,650,000,000 km 0.001089 degrees ?
Neptune 4,324,000,000 km 0.000653 degrees ?
We are ultimately going to use these planetary diameters to construct a giant scale model of the Solar System.