<p>Thanks to the Mercury transit, you can measure the parallax from the Earth. That happens due to <a href="https://en.wikipedia.org/wiki/TRACE" rel="noreferrer">TRACE</a> , which tracks the transit of Mercury along the polar diameter of the Earth.</p>

<p><a href="https://i.sstatic.net/ly8dF.png" rel="noreferrer"><img src="https://i.sstatic.net/ly8dF.png" alt="NASA/IMAGE"></a></p>

<p>During that tracking, the transit of Mercury goes like that:</p>

<p>[<img src="https://i.sstatic.net/200e9.png" alt="Lockheed Martin/TRACE[2]"></p>

<p>Now notice that, if TRACE remained stationary, the transit would be a straight line. So, if you calculate the maximum separation <em>vertically</em> of the center of Mercury and divide by two (how it's another different story), you got the parallax angle <span class="math-container">$\theta$</span>:</p>

<p><a href="https://i.sstatic.net/LiQev.png" rel="noreferrer"><img src="https://i.sstatic.net/LiQev.png" alt="Lockheed Martin/TRACE"></a></p>

<p>You know <span class="math-container">$\theta$</span>, you know Earth radius, so you know D, the distance from Earth to Mercury (in km) because</p>

<p><span class="math-container">$$\tan\theta = R/D$$</span></p>

<p>Now, if you wanna know how many km a AU is, just realise that Mercury is 0.56 AU from us, so divide D/0.56 and you got it!</p>

<p>All images credited to NASA/IMAGE and/or Lockheed Martin/TRACE</p>

CC BY-SA 4.0
2020-02-04T08:47:52.430Z
Please credit the [image source](https://image.gsfc.nasa.gov/poetry/transits/TRACEmerc.html) and explain what [TRACE](https://science.nasa.gov/missions/trace) was.
Mike G
CC BY-SA 4.0
2020-02-04T10:54:56.580Z
This is an interesting answer, but links break and rot over time, so it would be great if you included a discussion of what TRACE is rather than make each reader go off site. Thanks! btw I can't figure out why the heck that transit trajectory is wiggly in that way. It really does need to be explained.
uhoh
CC BY-SA 4.0
2020-02-04T11:29:13.450Z
The transit trajectory (seen from Earth) is not wiggly, but it is the sight from TRACE. It's wiggly because of the position of the spacecraft, the norther it is the further down the disk goes, and vice versa. We see an ondulation because I assume that TRACE makes several revolutions to the Earth, not just one, so it goes up and down and up and down, etc.
Carlos Vázquez Monzón
CC BY-SA 4.0
2020-02-04T13:08:33.880Z
Oh! I understand. Because of the its [sun synchronous orbit](https://en.wikipedia.org/wiki/Sun-synchronous_orbit) the Sun (and Mercury) are continuously visible as the spacecraft circled the Earth about three times! Okay got it. So was that an accident, or did they plan it that way?
uhoh
CC BY-SA 4.0
2020-02-04T20:16:04.193Z
Thank you for your answer, but why is theta divided by two?
Khanrad
CC BY-SA 4.0
2020-02-04T20:40:49.387Z
Because $\theta$ is measured like in the picture, and you calculate the maximum separation that spans from the south Pole to the north Pole, so, you need to divide by two
Carlos Vázquez Monzón
CC BY-SA 4.0
2020-02-04T08:09:33.873Z
2020-02-04T09:04:52.243Z
2020-02-04T09:04:52.243Z
Carlos Vázquez Monzón
<p>I am trying to use the transit of Mercury to estimate the distance between the Earth and the Sun, or 1 AU. </p>

<p>I know that I need to observe mercury from two antipodes, but I do not understand any of the underlying math behind this, or how to derive the astronomical unit from this.</p>

<p>Any help is appreciated!</p>

<amateur-observing><mercury><planetary-transits><astrometry><parallax>
How could one use the transit of Mercury to try and find the Astronomical Unit?
Khanrad
# How could one use the transit of Mercury to try and find the Astronomical Unit?

(Asked by: username_0 on 2020-02-03)

I am trying to use the transit of Mercury to estimate the distance between the Earth and the Sun, or 1 AU.

I know that I need to observe mercury from two antipodes, but I do not understand any of the underlying math behind this, or how to derive the astronomical unit from this.

Any help is appreciated!

**Tags:** amateur-observing, mercury, planetary-transits, astrometry, parallax

---

## 1 answers

### Answer by username_1 on 2020-02-04. Score: 5 | Accepted answer

Thanks to the Mercury transit, you can measure the parallax from the Earth. That happens due to [TRACE](https://en.wikipedia.org/wiki/TRACE) , which tracks the transit of Mercury along the polar diameter of the Earth.

[![NASA/IMAGE](https://i.sstatic.net/ly8dF.png)](https://i.sstatic.net/ly8dF.png)

During that tracking, the transit of Mercury goes like that:

[![Lockheed Martin/TRACE[2]](https://i.sstatic.net/200e9.png)

Now notice that, if TRACE remained stationary, the transit would be a straight line. So, if you calculate the maximum separation *vertically* of the center of Mercury and divide by two (how it's another different story), you got the parallax angle $\theta$:

[![Lockheed Martin/TRACE](https://i.sstatic.net/LiQev.png)](https://i.sstatic.net/LiQev.png)

You know $\theta$, you know Earth radius, so you know D, the distance from Earth to Mercury (in km) because

$$\tan\theta = R/D$$

Now, if you wanna know how many km a AU is, just realise that Mercury is 0.56 AU from us, so divide D/0.56 and you got it!

All images credited to NASA/IMAGE and/or Lockheed Martin/TRACE

> **Comments:**
> **username_2**: Please credit the [image source](https://image.gsfc.nasa.gov/poetry/transits/TRACEmerc.html) and explain what [TRACE](https://science.nasa.gov/missions/trace) was.  
> **username_3**: This is an interesting answer, but links break and rot over time, so it would be great if you included a discussion of what TRACE is rather than make each reader go off site. Thanks! btw I can't figure out why the heck that transit trajectory is wiggly in that way. It really does need to be explained.  
> **username_1**: The transit trajectory (seen from Earth) is not wiggly, but it is the sight from TRACE. It's wiggly because of the position of the spacecraft, the norther it is the further down the disk goes, and vice versa. We see an ondulation because I assume that TRACE makes several revolutions to the Earth, not just one, so it goes up and down and up and down, etc.  
> **username_3**: Oh! I understand. Because of the its [sun synchronous orbit](https://en.wikipedia.org/wiki/Sun-synchronous_orbit) the Sun (and Mercury) are continuously visible as the spacecraft circled the Earth about three times! Okay got it. So was that an accident, or did they plan it that way?  
> **username_0**: Thank you for your answer, but why is theta divided by two?  
> **username_1**: Because $\theta$ is measured like in the picture, and you calculate the maximum separation that spans from the south Pole to the north Pole, so, you need to divide by two  

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