<p>No, because the distance that the sun moves on the paper (s) is not the length of the arc that you have moved as the Earth rotates.  It is the length of an arc with centre at the sun spotter and radius = distance from sun spotter to paper.</p>
<p>Your formula would only find how far your sun spotter is from the paper on which you are projecting the sun. For example if s=3 inches and theta= 15 degrees (or 0.26 rad) then you would find r= 11.5 inches, and that is obviously not the radius of the Earth!</p>

CC BY-SA 4.0
2024-04-12T05:24:26.213Z
Although you haven't invented a way to measure the Earth, you have invented an excellent clock,  unfortunately the ancient Egyptians and Babylonians got there first.
James K
CC BY-SA 4.0
2024-04-12T13:10:17.493Z
You can determine the radius of the Earth from observations of the Sun. Look up Eratosthenes online. I just looked and got over 5 million results. He got a number very close to what we now know.  His math was sound but he was lucky in having his measurement errors cancel one another.
stretch
CC BY-SA 4.0
2024-04-12T13:43:03.870Z
While yes, that's a very different method. If I have my ancient greeks straight, then he put two equal-length sticks in the ground vertically, and measured shadow lengths on the longest day of the year. Most relevantly, he did this at different latitudes, then calculated with triangles. It's fundamentally impossible to use that method when in one location.
Gloweye
CC BY-SA 4.0
2024-04-12T15:31:29.280Z
So it *is* possible to do what the question title says, but not with the method in the question. @stretch
Barmar
CC BY-SA 4.0
2024-04-13T21:00:50.730Z
@Barmar  It's not possible to determine the radius of the Earth by observations in only one location.  You need to observe from two different locations to determine the radius.
James K
CC BY-SA 4.0
2024-04-15T06:44:03.053Z
@JamesK Exactly, as Gloweye already said. But it's still "using the sun".
Barmar
CC BY-SA 4.0
2024-04-12T05:21:45.120Z
2024-04-12T05:21:45.120Z
James K
<p>Can someone tell me why this would or would not work?</p>
<p>I have a sun spotter device that projects an image of the sun onto a piece of paper using a lens and some mirrors. When you use the device it’s quite clear that the sun moves across the image pretty quickly due to the earths rotation. This got me thinking: I can measure (on the paper) how many inches the sun shifts over some timescale, and divide that timescale by 24 hours. This should be the angle that the earth turned through. Then i can use s = r theta and solve for r, where s is the length that i measured and theta is the angle. Should this work?</p>
<p>I’m unsure because the earth rotates quite quickly, and the image of the sun only shifts slightly. Perhaps the lens makes things difficult</p>

CC BY-SA 4.0
2024-04-12T04:50:55.803Z
It's not clear what your sun spotter is doing. A diagram would help. Is it like this? https://www.scientificsonline.com/product/sunspotter
PM 2Ring
CC BY-SA 4.0
2024-04-12T04:54:18.007Z
*"the earth rotates quite quickly"* Indeed! At the equator, the rotation speed is ~465 m/s, and about half that at latitude 60°. Obviously, your sun spotter image, or shadows on a sundial, don't move at that speed. ;)
PM 2Ring
CC BY-SA 4.0
2024-04-12T16:12:58.207Z
This seems like a very simple experiment to run. When you did it, what did you come up with? Did your answer make sense?
Darth Pseudonym
CC BY-SA 4.0
2024-04-12T16:29:07.660Z
You've essentially made a sundial.  You could, in theory, measure the angle the Sun moved and measure the distance the image moves, but doing so over a short distance is going to have a lot of error margin.  It is essentially what Eratosthenes did, but over a much, much larger distance.
Greg Miller
<observational-astronomy><earth><distances><angular-distance>
Measure the radius of the earth using the sun?
James Thiamin
# Measure the radius of the earth using the sun?

(Asked by: username_0 on 2024-04-12)

Can someone tell me why this would or would not work?

I have a sun spotter device that projects an image of the sun onto a piece of paper using a lens and some mirrors. When you use the device it’s quite clear that the sun moves across the image pretty quickly due to the earths rotation. This got me thinking: I can measure (on the paper) how many inches the sun shifts over some timescale, and divide that timescale by 24 hours. This should be the angle that the earth turned through. Then i can use s = r theta and solve for r, where s is the length that i measured and theta is the angle. Should this work?

I’m unsure because the earth rotates quite quickly, and the image of the sun only shifts slightly. Perhaps the lens makes things difficult

**Tags:** observational-astronomy, earth, distances, angular-distance
> **Comments:**
> **username_1**: It's not clear what your sun spotter is doing. A diagram would help. Is it like this? https://www.scientificsonline.com/product/sunspotter  
> **username_1**: *"the earth rotates quite quickly"* Indeed! At the equator, the rotation speed is ~465 m/s, and about half that at latitude 60°. Obviously, your sun spotter image, or shadows on a sundial, don't move at that speed. ;)  
> **username_2**: This seems like a very simple experiment to run. When you did it, what did you come up with? Did your answer make sense?  
> **username_3**: You've essentially made a sundial.  You could, in theory, measure the angle the Sun moved and measure the distance the image moves, but doing so over a short distance is going to have a lot of error margin.  It is essentially what Eratosthenes did, but over a much, much larger distance.  

---

## 1 answers

### Answer by username_4 on 2024-04-12. Score: 6

No, because the distance that the sun moves on the paper (s) is not the length of the arc that you have moved as the Earth rotates. It is the length of an arc with centre at the sun spotter and radius = distance from sun spotter to paper.

Your formula would only find how far your sun spotter is from the paper on which you are projecting the sun. For example if s=3 inches and theta= 15 degrees (or 0.26 rad) then you would find r= 11.5 inches, and that is obviously not the radius of the Earth!

> **Comments:**
> **username_4**: Although you haven't invented a way to measure the Earth, you have invented an excellent clock,  unfortunately the ancient Egyptians and Babylonians got there first.  
> **username_5**: You can determine the radius of the Earth from observations of the Sun. Look up Eratosthenes online. I just looked and got over 5 million results. He got a number very close to what we now know.  His math was sound but he was lucky in having his measurement errors cancel one another.  
> **username_6**: While yes, that's a very different method. If I have my ancient greeks straight, then he put two equal-length sticks in the ground vertically, and measured shadow lengths on the longest day of the year. Most relevantly, he did this at different latitudes, then calculated with triangles. It's fundamentally impossible to use that method when in one location.  
> **username_7**: So it *is* possible to do what the question title says, but not with the method in the question. @stretch  
> **username_4**: @Barmar  It's not possible to determine the radius of the Earth by observations in only one location.  You need to observe from two different locations to determine the radius.  
> **username_7**: @JamesK Exactly, as Gloweye already said. But it's still "using the sun".  

---

