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wrote...
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2 months ago
Sorry if this is in the wrong forum.  So we all know that the Sun is approximately 93M miles away, but how exactly did they calculate this?
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wrote...
2 months ago
Since 1961, we transmit a radar signal at another planet (or moon or asteroid) and measure how long it takes for the radar echo to return.
wrote...
2 months ago
By observation of parallax.

Edmund Halley (of comet fame) was the first to come up with the idea to determine the Sun's distance by observing the transit of Venus.

A transit of Venus means we are watching Venus pass in front of the Sun.

Parallax is the effect whereby the position or direction of an object appears to differ when viewed from different positions.

So, Halley figured that two observers on Earth, if in different locations, would see Venus cross the Sun at a slightly different time, because of parallax.  The effect is exaggerated in this picture:



In this picture (assume Venus is moving counterclockwise about the Sun) we can see that a person a point A on Earth would see the transit as just starting while a person a point B on Earth would see the transit just finishing. 

Halley knew, based on astronomical observations, that the distance between the Sun and Venus was 0.72 times the distance between the Sun and Earth.  So, he figured if we knew the distance between A and B and could calculate theta, we could use trigonometry to determine the distance between Earth and the Sun.

It turned out that it wasn't possible to get the required accuracy of measurements this way, so it was determined that rather than taking measurements at one point in time, they could measure the time of each transit, because one perceived transit would be shorter than the other, as depicted in this picture:



Theta could be solved from this by using the Pythagorean Theorem:



The radius of the sun is phrased in arcminutes based on observation to be 15.25 arcminutes.  The drift rate is just the number of degrees in a circle (360) divided by the number of days to orbit the sun (224 for Venus) and then convert the units from days down to seconds).

In 1761, scientists had an opportunity to test this out, and their results were within 2.6% of the actual distance.

In 2012 there was another Venus transit.  This is a picture of the transit.

wrote...
2 months ago Edited: 2 months ago, ajac63
By observation of parallax. Edmund Halley (of comet fame) was the first to come up with the idea to determine the Sun's distance by observing the transit of Venus. A transit of Venus means we are watching Venus pass in front of the Sun. Parallax is the effect whereby the position or direction of an object appears to differ when viewed from different positions. So, Halley figured that two observers on Earth, if in different locations, would see Venus cross the Sun at a slightly different time, because of parallax. The effect is exaggerated in this picture: In this picture (assume Venus is moving counterclockwise about the Sun) we can see that a person a point A on Earth would see the transit as just starting while a person a point B on Earth would see the transit just finishing. Halley knew, based on astronomical observations, that the distance between the Sun and Venus was 0.72 times the distance between the Sun and Earth. So, he figured if we knew the distance between A and B and could calculate theta, we could use trigonometry to determine the distance between Earth and the Sun. It turned out that it wasn't possible to get the required accuracy of measurements this way, so it was determined that rather than taking measurements at one point in time, they could measure the time of each transit, because one perceived transit would be shorter than the other, as depicted in this picture: Theta could be solved from this by using the Pythagorean Theorem: The radius of the sun is phrased in arcminutes based on observation to be 15.25 arcminutes. The drift rate is just the number of degrees in a circle (360) divided by the number of days to orbit the sun (224 for Venus) and then convert the units from days down to seconds). In 1761, scientists had an opportunity to test this out, and their results were within 2.6% of the actual distance. In 2012 there was another Venus transit. This is a picture of the transit.

Thanks for the detailed explanation which jogs my memory back to my high school days a bit.  So, Halley knew based on astronomical observations with a telescope, in the 1720s or thereabouts?  Were telescopes that good yet?  And how did he know that the distance between the Sun and Venus was .72 times the distance between the Sun and the Earth when he didn't know yet what the latter distance was?
Post Merge: 2 months ago

Since 1961, we transmit a radar signal at another planet (or moon or asteroid) and measure how long it takes for the radar echo to return.
Yes, but wouldn't much of the radar signal be absorbed by a star?  How would any signal return; wouldn't the signal would be very weak?
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wrote...
2 months ago
Quote
Thanks for the detailed explanation which jogs my memory back to my high school days a bit.

welcome Slight Smile

So, Halley knew based on astronomical observations with a telescope, in the 1720s or thereabouts?

Yes

Were telescopes that good yet?

Guessing the error of 2.6% accounted for human error and equipment limitations

And how did he know that the distance between the Sun and Venus was .72 times the distance between the Sun and the Earth when he didn't know yet what the latter distance was?

The distance between Venus and the Sun equals 0.72 times the distance between Earth and Sun from Kepler’s third law. -- go to page 37 in the document below for a better visual of the math

Quote
Yes, but wouldn't much of the radar signal be absorbed by a star?  How would any signal return; wouldn't the signal would be very weak?

Radar is bounced off of venus, and extrapolated from that, don't know the details too well (see source)
Source https://pages.uoregon.edu/soper/Sun/distance.html
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wrote...
2 months ago
OK, thanks, that clears it up a lot for me, although there's still a few questions, mainly to do with if telescopic equipment in Halley's time was good enough and if we had radar transmitters powerful enough to send a signal to Pluto and back again.
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wrote...
Staff Member
2 months ago Edited: 2 months ago, duddy
OK, thanks, that clears it up a lot for me, although there's still a few questions, mainly to do with if telescopic equipment in Halley's time was good enough and if we had radar transmitters powerful enough to send a signal to Pluto and back again.

That's a great question, I'd really like to know how they calculated the distance known today between Earth and Pluto. I'm certain no radar exists to accomplish this, given that it's too deep in space. I couldn't find a video on YouTube either; I need to create one for the team.
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wrote...
Educator
2 months ago Edited: 2 months ago, bio_man
I'd be interested in creating an explanation video for how the Venus' distance and the sun's was calculated!
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wrote...
2 months ago
I'd be interested in creating an explanation video for how the Venus' distance and the sun's was calculated!

How ar eyou going to animate it ?

Good article: https://en.wikipedia.org/wiki/1639_transit_of_Venus
wrote...
Educator
2 months ago
I'd be interested in creating an explanation video for how the Venus' distance and the sun's was calculated!
How ar eyou going to animate it ? Good article: https://en.wikipedia.org/wiki/1639_transit_of_Venus

I'll explain it mathematically with some drawings
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wrote...
A month ago Edited: A month ago, ajac63
OK, thanks, that clears it up a lot for me, although there's still a few questions, mainly to do with if telescopic equipment in Halley's time was good enough and if we had radar transmitters powerful enough to send a signal to Pluto and back again.
That's a great question, I'd really like to know how they calculated the distance known today between Earth and Pluto. I'm certain no radar exists to accomplish this, given that it's too deep in space. I couldn't find a video on YouTube either; I need to create one for the team.
Sorry for late reply only I've had Internet connection issues...  Anyway, this is more or less what I was thinking as well, that even today, never mind then, we don't have radar equipment powerful enough to send a signal to Venus (I meant Venus last time, not Pluto...), and even if we did, how would the signal get back again intact with the radiation belt in the way?
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Educator
A month ago
The signal would most likely dissipate if we're trying to capture it from Earth.; our atmosphere is too protective.

That's why it's done in outer space, namely from the space station or a flying saucer/space probe.
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Staff Member
A month ago
and even if we did, how would the signal get back again intact with the radiation belt in the way?

Exactly, it wouldn't

Most of our measurements have come from probes that skim past the planet
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- Bachelor of Science (Biology)
- Bachelor of Education
wrote...
A month ago Edited: A month ago, ajac63
The signal would most likely dissipate if we're trying to capture it from Earth.; our atmosphere is too protective. That's why it's done in outer space, namely from the space station or a flying saucer/space probe.
More Internet connection probs, sorry for late reply...  I think it would dissipate because how would any signal bounced off Venus (forget the Sun) get to just the radiation belt, never mind through it, without signal amplification or boosting?  By space station, you mean the ISS?  Allegedly we knew that the Sun was 93m miles away well before the ISS.
Post Merge: A month ago

and even if we did, how would the signal get back again intact with the radiation belt in the way?
Exactly, it wouldn't Most of our measurements have come from probes that skim past the planet
Probes that skim past the Earth?
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