<p>Below <a href="https://astronomy.stackexchange.com/a/37124/7982">this answer</a> to <em>Why are Delta Aquariids “for the southern hemisphere” while the Perseids are “for the north”?</em> I wrote the <a href="https://astronomy.stackexchange.com/questions/37122/why-are-delta-aquariids-for-the-southern-hemisphere-while-the-perseids-are-fo#comment74052_37124">comment</a>:</p>
<blockquote>
<p><code>+1</code> To make this complete, <a href="https://en.wikipedia.org/wiki/Comet_Swift%E2%80%93Tuttle" rel="nofollow noreferrer">Comet Swift-Tuttle</a> has a nearly circular orbit of about 1 AU but an inclination of <strong>113.45°</strong> which is just about what it would have to be (double) to push the Perseids' radiant to a declination of +58°.</p>
</blockquote>
<p>Now I'm thinking that a vector that points toward's a meteor shower's radiant is just the vector sum of the Earth's orbit's velocity vector and the velocity vector associated with the orbit of the shower's associated comet at their intersection point where the shower is a maximum.</p>
<p><strong>Question:</strong> If that's the case, is there a simple set of equations for the position of a meteor shower's radiant point  and a source for them that can be cited?</p>
<p>It seems like this would have been done quite a long time ago and should be found in some classic early work!</p>
<p><strong>note:</strong> As discussed in comments, rewriting &quot;just the vector sum of the Earth's orbit's velocity vector and the velocity vector associated with the orbit of the shower's associated comet at their intersection point&quot; as <span class="math-container">$\mathbf{\vec{r}} = \mathbf{\vec{e}} + \mathbf{\vec{c}}$</span> doesn't help as we still need the same amount of information.</p>
<p>I wonder if the early work on radiant celestial coordinates and comets contain some interesting math based on Keplerian elements - we have the information that the two orbits <em>intersect</em> and we know where it happens (because of the date) <strong>so there is substantial reduction in the number of independent variables.</strong></p>
<hr />
<hr />
<p>For additional reading and resources about the relationship between a meteor shower and it's associated comet's orbit, see:</p>
<ul>
<li><a href="https://astronomy.stackexchange.com/q/35919/7982">Why do particles from a comet that result in meteor showers spread out mostly along the comet&#39;s orbit?</a></li>
<li><a href="https://astronomy.stackexchange.com/q/35923/7982">Have meteor showers been predicted for planets or solar-system bodies other than Earth? Have attempts been made to detect them?</a></li>
<li><a href="https://astronomy.stackexchange.com/q/35914/7982">How can comets have tails if there&#39;s no air resistance in space?</a></li>
<li><a href="https://astronomy.stackexchange.com/q/27301/7982">Why would the Perseids meteor rate fall off after maximum faster than the increase before maximum?</a></li>
<li><a href="https://astronomy.stackexchange.com/q/23555/7982">Meteor shower predicted to be best viewed BEFORE midnight (for reasons other than the moon)?</a></li>
<li><a href="https://astronomy.stackexchange.com/q/34018/7982">What makes some meteor showers continue for days, while the &quot;Unicorn shower&quot; can be shorter than one hour?</a></li>
<li><a href="https://astronomy.stackexchange.com/q/25582/7982">How significant are the recent results that Scholz’s Star has perturbed several observed hyperbolic objects?</a></li>
<li><a href="https://astronomy.stackexchange.com/q/35922/7982">https://astronomy.stackexchange.com/q/35922/7982</a></li>
<li><a href="https://astronomy.stackexchange.com/q/20597/7982">Why are these objects moving at Vastly Different Speeds along the same orbit?</a></li>
</ul>

CC BY-SA 4.0
2023-07-02T04:42:06.273Z
I'm not clear on what you're asking for, as it's hard to get any more simple than $ radiant = \vec{e} + \vec{m} $.  If you're looking for sources, you might have better luck searching for information on computing the parent body's orbit from the radiant, because that's the more common problem.  We observe the meteor direction and velocity, subtract off the Earth's velocity, and compute the parent body's orbit from that.
Greg Miller
CC BY-SA 4.0
2023-07-02T04:42:58.393Z
@GregMiller hang on I'll take a look right now (it's been 3 years...)
uhoh
CC BY-SA 4.0
2023-07-02T04:45:58.930Z
@GregMiller I did write "Now I'm thinking that a vector that points toward's a meteor shower's radiant is just the vector sum of the Earth's orbit's velocity vector and the velocity vector associated with the orbit of the shower's associated comet at their intersection point where the shower is a maximum." and later "**Question:** If that's the case, is there a simple set of equations for the position of a meteor shower's radiant point and a source for them that can be cited?"
uhoh
CC BY-SA 4.0
2023-07-02T04:46:49.740Z
@GregMiller So it looks like the title doesn't do a good job of summarizing the actual question that I've asked (and readers should read!). I'll update the title to better match the actual question post. Is there anything about the post itself that leaves the question still unclear for you? I'll add the post that r = e + c (c=original comet) isn't really a "simple equation" to me in this context since there is still the problem of finding e and c. Give me an hour; I just [asked a long question elsewhere](https://codereview.stackexchange.com/q/285864/145009) and need some oxygen + coffee.
uhoh
CC BY-SA 4.0
2023-07-02T15:02:05.190Z
While finding "e" and "c" are far from trivial, they are solved problems.  For example, the velocity of the Earth can be obtained using the JPL Development Ephemeris, or VSOP87.  The position and velocity of the comet partcles can be obtained by solving Kepler's equation.  I'm not sure it's worthwhile to repeat how to do those here.
Greg Miller
CC BY-SA 4.0
2023-07-03T03:59:31.163Z
@GregMiller then you are welcome to move on and look for other questions that you feel are worthwhile for you. Thanks!
uhoh
<solar-system><orbital-mechanics><comets><history><meteor-shower>
RA/Dec of a meteor shower's radiant point based on its associated comet's orbit; simple set of equations? "Classic" early reference to cite?
uhoh
# RA/Dec of a meteor shower's radiant point based on its associated comet's orbit; simple set of equations? "Classic" early reference to cite?

(Asked by: username_0 on 2020-07-25)

Below [this answer](https://astronomy.stackexchange.com/a/37124/7982) to *Why are Delta Aquariids “for the southern hemisphere” while the Perseids are “for the north”?* I wrote the [comment](https://astronomy.stackexchange.com/questions/37122/why-are-delta-aquariids-for-the-southern-hemisphere-while-the-perseids-are-fo#comment74052_37124):

> `+1` To make this complete, [Comet Swift-Tuttle](https://en.wikipedia.org/wiki/Comet_Swift%E2%80%93Tuttle) has a nearly circular orbit of about 1 AU but an inclination of **113.45°** which is just about what it would have to be (double) to push the Perseids' radiant to a declination of +58°.

Now I'm thinking that a vector that points toward's a meteor shower's radiant is just the vector sum of the Earth's orbit's velocity vector and the velocity vector associated with the orbit of the shower's associated comet at their intersection point where the shower is a maximum.

**Question:** If that's the case, is there a simple set of equations for the position of a meteor shower's radiant point and a source for them that can be cited?

It seems like this would have been done quite a long time ago and should be found in some classic early work!

**note:** As discussed in comments, rewriting "just the vector sum of the Earth's orbit's velocity vector and the velocity vector associated with the orbit of the shower's associated comet at their intersection point" as $\mathbf{\vec{r}} = \mathbf{\vec{e}} + \mathbf{\vec{c}}$ doesn't help as we still need the same amount of information.

I wonder if the early work on radiant celestial coordinates and comets contain some interesting math based on Keplerian elements - we have the information that the two orbits *intersect* and we know where it happens (because of the date) **so there is substantial reduction in the number of independent variables.**

---

---

For additional reading and resources about the relationship between a meteor shower and it's associated comet's orbit, see:

* [Why do particles from a comet that result in meteor showers spread out mostly along the comet's orbit?](https://astronomy.stackexchange.com/q/35919/7982)
* [Have meteor showers been predicted for planets or solar-system bodies other than Earth? Have attempts been made to detect them?](https://astronomy.stackexchange.com/q/35923/7982)
* [How can comets have tails if there's no air resistance in space?](https://astronomy.stackexchange.com/q/35914/7982)
* [Why would the Perseids meteor rate fall off after maximum faster than the increase before maximum?](https://astronomy.stackexchange.com/q/27301/7982)
* [Meteor shower predicted to be best viewed BEFORE midnight (for reasons other than the moon)?](https://astronomy.stackexchange.com/q/23555/7982)
* [What makes some meteor showers continue for days, while the "Unicorn shower" can be shorter than one hour?](https://astronomy.stackexchange.com/q/34018/7982)
* [How significant are the recent results that Scholz’s Star has perturbed several observed hyperbolic objects?](https://astronomy.stackexchange.com/q/25582/7982)
* <https://astronomy.stackexchange.com/q/35922/7982>
* [Why are these objects moving at Vastly Different Speeds along the same orbit?](https://astronomy.stackexchange.com/q/20597/7982)

**Tags:** solar-system, orbital-mechanics, comets, history, meteor-shower
> **Comments:**
> **username_1**: I'm not clear on what you're asking for, as it's hard to get any more simple than $ radiant = \vec{e} + \vec{m} $.  If you're looking for sources, you might have better luck searching for information on computing the parent body's orbit from the radiant, because that's the more common problem.  We observe the meteor direction and velocity, subtract off the Earth's velocity, and compute the parent body's orbit from that.  
> **username_0**: @GregMiller hang on I'll take a look right now (it's been 3 years...)  
> **username_0**: @GregMiller I did write "Now I'm thinking that a vector that points toward's a meteor shower's radiant is just the vector sum of the Earth's orbit's velocity vector and the velocity vector associated with the orbit of the shower's associated comet at their intersection point where the shower is a maximum." and later "**Question:** If that's the case, is there a simple set of equations for the position of a meteor shower's radiant point and a source for them that can be cited?"  
> **username_0**: @GregMiller So it looks like the title doesn't do a good job of summarizing the actual question that I've asked (and readers should read!). I'll update the title to better match the actual question post. Is there anything about the post itself that leaves the question still unclear for you? I'll add the post that r = e + c (c=original comet) isn't really a "simple equation" to me in this context since there is still the problem of finding e and c. Give me an hour; I just [asked a long question elsewhere](https://codereview.stackexchange.com/q/285864/145009) and need some oxygen + coffee.  
> **username_1**: While finding "e" and "c" are far from trivial, they are solved problems.  For example, the velocity of the Earth can be obtained using the JPL Development Ephemeris, or VSOP87.  The position and velocity of the comet partcles can be obtained by solving Kepler's equation.  I'm not sure it's worthwhile to repeat how to do those here.  
> **username_0**: @GregMiller then you are welcome to move on and look for other questions that you feel are worthwhile for you. Thanks!  

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## 0 answers

