<p>From <a href="https://astronomy.stackexchange.com/questions/27423/what-is-the-difference-between-the-yarkovsky-effect-and-yorp-effect">What is the difference between the Yarkovsky effect and YORP effect?</a>, both the Yarkovsky and YORP effects describe the changes in momentum to a body in orbit due to the re-radiation of photons.  The Yarkovsky effect only describes the changes to the orbital parameters of the body:</p>
<blockquote>
<p>The Yarkovsky effect describes a small but significant force that
affects the orbital motion of meteoroids and asteroids</p>
</blockquote>
<p>The YORP effect only describes the changes to the rotational momentum of the body:</p>
<blockquote>
<p>This rotational variant has been coined the
Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect</p>
</blockquote>
<p>Consider a perfect uniform sphere in orbit around the Sun.  For any point on the sphere, the average direction of re-radiated photons will be normal to the local tangent plane (or directly opposite the center of gravity). In this case, we expect a Yarkovsky effect (change in orbital parameters), but no YORP effect (change in rotational momentum). Graphic from this <a href="https://www.boulder.swri.edu/%7Ebottke/Reprints/Bottke_2006_Ann_Rev_Earth_Planet_34.157.Yarkovsky_YORP.pdf" rel="nofollow noreferrer">source</a>.</p>
<p><a href="https://i.sstatic.net/FbzPL.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/FbzPL.png" alt="enter image description here" /></a></p>
<p>In contrast, consider an irregular body with a huge flat face offset from the center of gravity.  When photons are re-radiated from the flat face, on average they will impart some angular momentum change (YORP effect) and some orbital parameter change (Yarkovsky effect).</p>
<p><a href="https://i.sstatic.net/fLfiE.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/fLfiE.png" alt="enter image description here" /></a></p>
<blockquote>
<p>Yarkovsky only considers the center of mass recoil from thermal
radiation of a rotating body in sunlight, is YORP just the tangential
component of this recoil?</p>
</blockquote>
<p>The forces causing the YORP and Yarkovsky effects are not tangential in general. For a recoil for some impulse on a sphere, the rotational and linear forces imparted are tangential.  However, for an irregular shape like a rod, we wouldn't expect the two forces to be tangential. Here is a little drawing (extremely exaggerated for effect):</p>
<p><a href="https://i.sstatic.net/n92uA.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/n92uA.png" alt="enter image description here" /></a></p>
<p>In the above drawing, the Yarkovsky vector represents purely translational momentum change and the YORP vector represents purely rotational momentum change. The sum of the vectors that represent forces that cause the YORP and Yarkovsky effects should sum to the mass recoil vector (which is the negative of the impulse):</p>
<p><a href="https://i.sstatic.net/Dlq9f.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Dlq9f.png" alt="enter image description here" /></a></p>
<p>They YORP and Yarkovsky forces don't necessarily need to be at right angles.  In three dimensions, sorting out the forces can get extremely complicated.    <a href="https://physics.stackexchange.com/questions/116653/elastic-collision-of-point-particle-and-rod/170308#170308">It can be quite complicated for a rod even if the reaction mass vector is at the tip</a>. It's hard for me to imagine the recoil from a &quot;crescent moon&quot; shaped asteroid that has a center of mass exterior to the asteroid body.</p>
<blockquote>
<p>Or does it require the body to be non-uniform in order to spin-up the
body?</p>
</blockquote>
<p>The body must be irregular in shape to spin it up.  A perfect sphere with a non-uniform surface would not be subject to the YORP effect.  This is as mentioned above, since on average, photon emission at a specific point will be 90 degrees from the tangent plane, effectively canceling all YORP effects from individual emissions.</p>
<blockquote>
<p>Would a uniform sphere in fact spin-down?</p>
</blockquote>
<p>Again, a sphere would not have any YORP effects because the average re-radiation vector would be perfectly opposite the center of mass.</p>
<p><strong>Note:</strong></p>
<p>When an asteroid strikes a planetary sized body in an inelastic collision, momentum is also conserved.  Some of the asteroid's momentum goes into rotational momentum of the body and some of the momentum goes into the momentum of the center of mass (equivalent to the orbital parameters).  I like this analogy for thinking about the Yarkovsky and YORP effects.</p>

CC BY-SA 4.0
2020-12-22T04:54:32.130Z
Thanks for your thorough answer! For a smooth biaxial *or especially a triaxial* ellipsoid of uniform density and uniform surface, where except in a few places the surface normal does not point directly away from the center of mass, I'm guessing that "net YORP" is still zero. As simply a thought experiment, and not part of the question asked here, nor a new question (yet) I'm wondering what the minimally complicated item is that does have a "net YORP".
uhoh
CC BY-SA 4.0
2020-12-22T04:55:45.417Z
Does it require irregularity, or could a triaxial ellipsoid rotating around its minor axis start YORPing if it had a couple of black dots? No need to answer, I'm just puzzling out loud. I will read further. *Thanks!*
uhoh
CC BY-SA 4.0
2020-12-22T05:00:38.613Z
@uhoh I don't know if you could design an ellipsoid to start YORPing.  I recall having read that ellipsoids don't get YORPed, but it's against my intuition.  I certainly didn't go out on that limb with this answer.  Black dots on a white background would certainly be the technique.  Albedo vs Emissivity.
Connor Garcia
CC BY-SA 4.0
2020-12-22T05:05:33.980Z
My dream is to have a type of question called "space golf" which is similar to [code golf](https://codegolf.stackexchange.com) except they are space related challenges. I can imagine a problem where the shape and it's albedo painting are defined by a set of polynomials of the user's choice, and the goal is who can get the most angular acceleration from the least number of coefficients or something crazy like that :-0
uhoh
CC BY-SA 4.0
2020-12-22T05:13:28.250Z
What is the most simply described object with the max YORP?  You have to know dimensions, orbit, emissivity, albedo, conductivity, shape, and initial revolution.  But the papers I looked at that described YORP have some pretty complex and computationally intensive calculations.
Connor Garcia
CC BY-SA 4.0
2020-12-22T05:15:19.517Z
Space Golf would be SWEET!  Design your Volcanoid and see how it does?
Connor Garcia
CC BY-SA 4.0
2020-12-29T22:41:57.443Z
Isn't the green "Torque" arrow drawn in the wrong direction? And why does it have such a strange elliptical shape?
uhoh
CC BY-SA 4.0
2020-12-30T00:24:12.203Z
@uhoh Yes the green "Torque" arrow is drawn in the wrong direction and it shouldn't be curved.  I apologize. I will get this corrected ASAP.
Connor Garcia
CC BY-SA 4.0
2020-12-30T04:58:24.570Z
I think for the purposes of this answer you can just add a parenthetical comment under the figure and leave it there. It's quite nice otherwise. As far as the original source of the image, that's up to you!
uhoh
CC BY-SA 4.0
2020-12-30T05:03:58.837Z
@uhoh Thanks. I am reworking the whole answer to also better address your original question if the force that causes the YORP effect is a tangential component of the force that causes the Yarkovsky effect.  I expect to finish "soon."
Connor Garcia
CC BY-SA 4.0
2020-12-21T22:59:02.643Z
2020-12-30T05:36:48.200Z
2020-12-30T05:36:48.200Z
Connor Garcia
<p><a href="https://astronomy.stackexchange.com/a/40485/7982">This answer</a> to <em>Where have all the Vulcanoids gone?</em> links to the aptly-titled <a href="https://ui.adsabs.harvard.edu/abs/2020AAS...23527701C/abstract" rel="nofollow noreferrer">The YORP Effect Can Efficiently Destroy 100 Kilometer Planetesimals At The Inner Edge Of The Solar System</a> which says in part:</p>
<blockquote>
<p>... The YORP effect destroys Vulcanoids by spinning them up so fast that the gravitational accelerations holding components of the body together are matched by centrifugal accelerations, this causes the body to rotationally fission. i.e break apart. We calculated the timescale of this fission process for a parent Vulcanoid and for each of their subsequent generational fragments. <strong>We show that objects with radii up to 100 kilometers in size are efficiently destroyed by the YORP effect doing so in a timescale that is much younger than the age of the Solar System</strong>...</p>
</blockquote>
<p>Tha answer also links to the explanation of the YROP effect in <a href="https://www.planetary.org/articles/20141211-the-yorp-effect-and-bennu" rel="nofollow noreferrer">The YORP Effect and Bennu
</a> which says:</p>
<blockquote>
<p>The YORP effect is a similar phenomenon that affects the rotation rate and pole orientation of an asteroid. YORP is an acronym that combines four scientist’s names: Yarkovsky, O’Keefe, Radzievskii, and Paddack. Building on the work of Yarkovsky, V. V. Radzievskii showed in 1954 that variations in albedo across the surface of a small body in space could increase its rotation rate. <strong>This phenomenon is essentially the <a href="https://en.wikipedia.org/wiki/Crookes_radiometer" rel="nofollow noreferrer">Crooke’s radiometer</a> effect.</strong> Stephen Paddack and John O’Keefe, who were separately working on the origin of tektites and interplanetary dust, went on to show that an object’s shape strongly influences the change in rotation. David Rubincam synthesized these ideas in 1999, and showed that <strong>YORP creates a thermal torque akin to a “windmill” effect on asteroids.</strong> This torque can modify the rotation rate and obliquity of an asteroid, depending on the external geometry of the body.</p>
</blockquote>
<p>This is frustrating because of course the Crooke's radiometer works by interacting with the molecules of the low pressure gas intentionally included inside the glass bulb, and not by radiation, but at least we get the idea that a net torque is produced due to a non-uniformity of some optical property.</p>
<p>Wikipedia's <a href="https://en.wikipedia.org/wiki/Yarkovsky%E2%80%93O%27Keefe%E2%80%93Radzievskii%E2%80%93Paddack_effect" rel="nofollow noreferrer">Yarkovsky–O'Keefe–Radzievskii–Paddack effect</a> works hard to try to explain but the explanation is long and I am not confident it's actually accurate.</p>
<p>Answers to <a href="https://astronomy.stackexchange.com/q/27423/7982">What is the difference between the Yarkovsky effect and YORP effect?</a> touch on this but do not answer this question.</p>
<p><strong>Question:</strong> What is the YORP effect exactly? Is it just the non-central component of the <a href="https://en.wikipedia.org/wiki/Yarkovsky_effect" rel="nofollow noreferrer">Yarkovsky effect</a>?</p>
<ul>
<li>Yarkovsky only considers the center of mass recoil from thermal radiation of a rotating body in sunlight, is YORP just the tangential component of this recoil?</li>
<li>Or does it require the body to be non-uniform in order to spin-up the body?</li>
<li>Would a uniform sphere in fact spin-down?</li>
</ul>

CC BY-SA 4.0
2020-12-19T00:30:27.753Z
[I think that we have no good tags for solar-system-evolution or asteroid-formation or asteroid-evolution. Should we?](https://astronomy.meta.stackexchange.com/q/648/7982)
uhoh
CC BY-SA 4.0
2020-12-22T10:27:07.663Z
@antispinwards ya the idiomatic humor was meant as light-hearted with the implicit assumption that we're all having fun here asking and answering but it may have been too oblique to succeed in ASCII. *Thanks!*
uhoh
<solar-system><asteroids><rotation><planetary-formation><asteroid-evolution>
What is the YORP effect exactly? Is it just the non-central component of the Yarkovsky effect?
uhoh
# What is the YORP effect exactly? Is it just the non-central component of the Yarkovsky effect?

(Asked by: username_0 on 2020-12-19)

[This answer](https://astronomy.stackexchange.com/a/40485/7982) to *Where have all the Vulcanoids gone?* links to the aptly-titled [The YORP Effect Can Efficiently Destroy 100 Kilometer Planetesimals At The Inner Edge Of The Solar System](https://ui.adsabs.harvard.edu/abs/2020AAS...23527701C/abstract) which says in part:

> ... The YORP effect destroys Vulcanoids by spinning them up so fast that the gravitational accelerations holding components of the body together are matched by centrifugal accelerations, this causes the body to rotationally fission. i.e break apart. We calculated the timescale of this fission process for a parent Vulcanoid and for each of their subsequent generational fragments. **We show that objects with radii up to 100 kilometers in size are efficiently destroyed by the YORP effect doing so in a timescale that is much younger than the age of the Solar System**...

Tha answer also links to the explanation of the YROP effect in [The YORP Effect and Bennu](https://www.planetary.org/articles/20141211-the-yorp-effect-and-bennu) which says:

> The YORP effect is a similar phenomenon that affects the rotation rate and pole orientation of an asteroid. YORP is an acronym that combines four scientist’s names: Yarkovsky, O’Keefe, Radzievskii, and Paddack. Building on the work of Yarkovsky, V. V. Radzievskii showed in 1954 that variations in albedo across the surface of a small body in space could increase its rotation rate. **This phenomenon is essentially the [Crooke’s radiometer](https://en.wikipedia.org/wiki/Crookes_radiometer) effect.** Stephen Paddack and John O’Keefe, who were separately working on the origin of tektites and interplanetary dust, went on to show that an object’s shape strongly influences the change in rotation. David Rubincam synthesized these ideas in 1999, and showed that **YORP creates a thermal torque akin to a “windmill” effect on asteroids.** This torque can modify the rotation rate and obliquity of an asteroid, depending on the external geometry of the body.

This is frustrating because of course the Crooke's radiometer works by interacting with the molecules of the low pressure gas intentionally included inside the glass bulb, and not by radiation, but at least we get the idea that a net torque is produced due to a non-uniformity of some optical property.

Wikipedia's [Yarkovsky–O'Keefe–Radzievskii–Paddack effect](https://en.wikipedia.org/wiki/Yarkovsky%E2%80%93O%27Keefe%E2%80%93Radzievskii%E2%80%93Paddack_effect) works hard to try to explain but the explanation is long and I am not confident it's actually accurate.

Answers to [What is the difference between the Yarkovsky effect and YORP effect?](https://astronomy.stackexchange.com/q/27423/7982) touch on this but do not answer this question.

**Question:** What is the YORP effect exactly? Is it just the non-central component of the [Yarkovsky effect](https://en.wikipedia.org/wiki/Yarkovsky_effect)?

* Yarkovsky only considers the center of mass recoil from thermal radiation of a rotating body in sunlight, is YORP just the tangential component of this recoil?
* Or does it require the body to be non-uniform in order to spin-up the body?
* Would a uniform sphere in fact spin-down?

**Tags:** solar-system, asteroids, rotation, planetary-formation, asteroid-evolution
> **Comments:**
> **username_0**: [I think that we have no good tags for solar-system-evolution or asteroid-formation or asteroid-evolution. Should we?](https://astronomy.meta.stackexchange.com/q/648/7982)  
> **username_0**: @antispinwards ya the idiomatic humor was meant as light-hearted with the implicit assumption that we're all having fun here asking and answering but it may have been too oblique to succeed in ASCII. *Thanks!*  

---

## 1 answers

### Answer by username_1 on 2020-12-21. Score: 3 | Accepted answer

From [What is the difference between the Yarkovsky effect and YORP effect?](https://astronomy.stackexchange.com/questions/27423/what-is-the-difference-between-the-yarkovsky-effect-and-yorp-effect), both the Yarkovsky and YORP effects describe the changes in momentum to a body in orbit due to the re-radiation of photons. The Yarkovsky effect only describes the changes to the orbital parameters of the body:

> The Yarkovsky effect describes a small but significant force that
> affects the orbital motion of meteoroids and asteroids

The YORP effect only describes the changes to the rotational momentum of the body:

> This rotational variant has been coined the
> Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect

Consider a perfect uniform sphere in orbit around the Sun. For any point on the sphere, the average direction of re-radiated photons will be normal to the local tangent plane (or directly opposite the center of gravity). In this case, we expect a Yarkovsky effect (change in orbital parameters), but no YORP effect (change in rotational momentum). Graphic from this [source](https://www.boulder.swri.edu/%7Ebottke/Reprints/Bottke_2006_Ann_Rev_Earth_Planet_34.157.Yarkovsky_YORP.pdf).

[![enter image description here](https://i.sstatic.net/FbzPL.png)](https://i.sstatic.net/FbzPL.png)

In contrast, consider an irregular body with a huge flat face offset from the center of gravity. When photons are re-radiated from the flat face, on average they will impart some angular momentum change (YORP effect) and some orbital parameter change (Yarkovsky effect).

[![enter image description here](https://i.sstatic.net/fLfiE.png)](https://i.sstatic.net/fLfiE.png)

> Yarkovsky only considers the center of mass recoil from thermal
> radiation of a rotating body in sunlight, is YORP just the tangential
> component of this recoil?

The forces causing the YORP and Yarkovsky effects are not tangential in general. For a recoil for some impulse on a sphere, the rotational and linear forces imparted are tangential. However, for an irregular shape like a rod, we wouldn't expect the two forces to be tangential. Here is a little drawing (extremely exaggerated for effect):

[![enter image description here](https://i.sstatic.net/n92uA.png)](https://i.sstatic.net/n92uA.png)

In the above drawing, the Yarkovsky vector represents purely translational momentum change and the YORP vector represents purely rotational momentum change. The sum of the vectors that represent forces that cause the YORP and Yarkovsky effects should sum to the mass recoil vector (which is the negative of the impulse):

[![enter image description here](https://i.sstatic.net/Dlq9f.png)](https://i.sstatic.net/Dlq9f.png)

They YORP and Yarkovsky forces don't necessarily need to be at right angles. In three dimensions, sorting out the forces can get extremely complicated. [It can be quite complicated for a rod even if the reaction mass vector is at the tip](https://physics.stackexchange.com/questions/116653/elastic-collision-of-point-particle-and-rod/170308#170308). It's hard for me to imagine the recoil from a "crescent moon" shaped asteroid that has a center of mass exterior to the asteroid body.

> Or does it require the body to be non-uniform in order to spin-up the
> body?

The body must be irregular in shape to spin it up. A perfect sphere with a non-uniform surface would not be subject to the YORP effect. This is as mentioned above, since on average, photon emission at a specific point will be 90 degrees from the tangent plane, effectively canceling all YORP effects from individual emissions.

> Would a uniform sphere in fact spin-down?

Again, a sphere would not have any YORP effects because the average re-radiation vector would be perfectly opposite the center of mass.

**Note:**

When an asteroid strikes a planetary sized body in an inelastic collision, momentum is also conserved. Some of the asteroid's momentum goes into rotational momentum of the body and some of the momentum goes into the momentum of the center of mass (equivalent to the orbital parameters). I like this analogy for thinking about the Yarkovsky and YORP effects.

> **Comments:**
> **username_0**: Thanks for your thorough answer! For a smooth biaxial *or especially a triaxial* ellipsoid of uniform density and uniform surface, where except in a few places the surface normal does not point directly away from the center of mass, I'm guessing that "net YORP" is still zero. As simply a thought experiment, and not part of the question asked here, nor a new question (yet) I'm wondering what the minimally complicated item is that does have a "net YORP".  
> **username_0**: Does it require irregularity, or could a triaxial ellipsoid rotating around its minor axis start YORPing if it had a couple of black dots? No need to answer, I'm just puzzling out loud. I will read further. *Thanks!*  
> **username_1**: @uhoh I don't know if you could design an ellipsoid to start YORPing.  I recall having read that ellipsoids don't get YORPed, but it's against my intuition.  I certainly didn't go out on that limb with this answer.  Black dots on a white background would certainly be the technique.  Albedo vs Emissivity.  
> **username_0**: My dream is to have a type of question called "space golf" which is similar to [code golf](https://codegolf.stackexchange.com) except they are space related challenges. I can imagine a problem where the shape and it's albedo painting are defined by a set of polynomials of the user's choice, and the goal is who can get the most angular acceleration from the least number of coefficients or something crazy like that :-0  
> **username_1**: What is the most simply described object with the max YORP?  You have to know dimensions, orbit, emissivity, albedo, conductivity, shape, and initial revolution.  But the papers I looked at that described YORP have some pretty complex and computationally intensive calculations.  
> **username_1**: Space Golf would be SWEET!  Design your Volcanoid and see how it does?  
> **username_0**: Isn't the green "Torque" arrow drawn in the wrong direction? And why does it have such a strange elliptical shape?  
> **username_1**: @uhoh Yes the green "Torque" arrow is drawn in the wrong direction and it shouldn't be curved.  I apologize. I will get this corrected ASAP.  
> **username_0**: I think for the purposes of this answer you can just add a parenthetical comment under the figure and leave it there. It's quite nice otherwise. As far as the original source of the image, that's up to you!  
> **username_1**: @uhoh Thanks. I am reworking the whole answer to also better address your original question if the force that causes the YORP effect is a tangential component of the force that causes the Yarkovsky effect.  I expect to finish "soon."  

---

