<p>My goal is to calculate the retrograde of Mercury. What I've been working from is the book, Practical Astronomy With Your Calculator 3rd edition. I've made some progress, but I seem to be stuck with how to get the right answer. Hopefully my data to work with is right. Here is a sample:</p>
<pre><code>Sat Feb 20 03:52:00 2021
Direct: 
Mercury: 160
Earth  : 77
Diff   : 83 : 237
Tue Jun 22 00:00:00 2021
Direct: 
Mercury: 358
Earth  : 199
Diff   : 159 : 557
Mon Oct 18 00:00:00 2021
Direct: 
Mercury: 124
Earth  : 314
Diff   : 190 : 438
</code></pre>
<p>All numbers are in degrees, based upon the main calculations from page 108. The calculations only cover part of the whole thing. Mostly to the bottom of page 108 #11. I then took the decimal part of the numbers I was getting for Vp and Ve, and converted that into degrees with a look up table. Also, I modified the formula in #2 to be Mercury's orbit period. Hoping to get more accurate data.</p>
<p>My question is: Can the angle between the two planets be calculated? I know the distance each planet is from the sun, but how can I get the angle between the two planets for the dates I've shown? I'm new to math like this, so forgive what I'm not aware of here.</p>
<p>Thank you!</p>
<p>See photo for formula used:
<a href="https://i.sstatic.net/e2QGn.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/e2QGn.jpg" alt="part 1" /></a></p>
<p><a href="https://i.sstatic.net/NTRtQ.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/NTRtQ.jpg" alt="calculations 2" /></a></p>

CC BY-SA 4.0
2021-05-05T09:34:30.387Z
It's a very good book ,but not everyone has the book at hand. Can you add here what exactly you are calculating and what the output numbers you show mean / what angles you calculated? What is the physical meaning of Ve and Vp you refer to? What is to you "the angle between those planets"? As seen from where?
planetmaker
CC BY-SA 4.0
2021-05-05T18:11:06.203Z
@planetmaker added photos of the calculations used. The angle between the two planets as seen from a heliocentric orbit, but maybe what I want is as seen from earth? I would think the angle would be the same in either, is that wrong?
Misfit
CC BY-SA 4.0
2021-05-09T02:08:32.460Z
For those who try doing this kind of stuff; there are two books to get. Practical Ephemeris Calculations, and Astronomy on the Personal Computer. Both books are by Montenbruck. He has all the calculation you could need for this stuff.
Misfit
<orbit><earth><mercury>
Calculating Angle Between Two Planets In Heliocentric Orbit
Misfit
# Calculating Angle Between Two Planets In Heliocentric Orbit

(Asked by: username_0 on 2021-05-05)

My goal is to calculate the retrograde of Mercury. What I've been working from is the book, Practical Astronomy With Your Calculator 3rd edition. I've made some progress, but I seem to be stuck with how to get the right answer. Hopefully my data to work with is right. Here is a sample:

```
Sat Feb 20 03:52:00 2021
Direct: 
Mercury: 160
Earth  : 77
Diff   : 83 : 237
Tue Jun 22 00:00:00 2021
Direct: 
Mercury: 358
Earth  : 199
Diff   : 159 : 557
Mon Oct 18 00:00:00 2021
Direct: 
Mercury: 124
Earth  : 314
Diff   : 190 : 438

```

All numbers are in degrees, based upon the main calculations from page 108. The calculations only cover part of the whole thing. Mostly to the bottom of page 108 #11. I then took the decimal part of the numbers I was getting for Vp and Ve, and converted that into degrees with a look up table. Also, I modified the formula in #2 to be Mercury's orbit period. Hoping to get more accurate data.

My question is: Can the angle between the two planets be calculated? I know the distance each planet is from the sun, but how can I get the angle between the two planets for the dates I've shown? I'm new to math like this, so forgive what I'm not aware of here.

Thank you!

See photo for formula used:
[![part 1](https://i.sstatic.net/e2QGn.jpg)](https://i.sstatic.net/e2QGn.jpg)

[![calculations 2](https://i.sstatic.net/NTRtQ.jpg)](https://i.sstatic.net/NTRtQ.jpg)

**Tags:** orbit, earth, mercury

> **Comments:**
> **username_1**: It's a very good book ,but not everyone has the book at hand. Can you add here what exactly you are calculating and what the output numbers you show mean / what angles you calculated? What is the physical meaning of Ve and Vp you refer to? What is to you "the angle between those planets"? As seen from where?  
> **username_0**: @username_1 added photos of the calculations used. The angle between the two planets as seen from a heliocentric orbit, but maybe what I want is as seen from earth? I would think the angle would be the same in either, is that wrong?  
> **username_0**: For those who try doing this kind of stuff; there are two books to get. Practical Ephemeris Calculations, and Astronomy on the Personal Computer. Both books are by Montenbruck. He has all the calculation you could need for this stuff.  

---

## 0 answers

