<p>Here is a screenshot of JPL SBDB's elements for asteroid <a href="https://ssd.jpl.nasa.gov/tools/sbdb_lookup.html#/?sstr=K21G02T" rel="nofollow noreferrer">2021 GT2</a>.
The perihelion time <strong>tp</strong> is shown as a Julian date on the TDB timescale with uncertainty in days.</p>
<p><a href="https://i.sstatic.net/6VF04.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/6VF04.png" alt="Screenshot of orbital elements from JPL SBDB" /></a></p>
<p>If I evaluate the <a href="https://minorplanetcenter.net/iau/info/UValue.html" rel="nofollow noreferrer">MPC formulas</a>:</p>
<pre><code>RUNOFF = (dT * e + 10 / P * dP) * ko / P * 3600 * 3

U = INT(ln(RUNOFF)/CONS)+1  (0 &lt;= U &lt;= 9)
</code></pre>
<p>with dT = 0.00022344 d, e = 0.23291, P = 0.93321 y, dP = 0.00028335 d,
ko = 0.98561°, and CONS = 1.4868,
I get RUNOFF = 35.227 and U = 3, matching JPL's &quot;condition code&quot; for this asteroid.
MPC's &quot;uncertainty&quot; for <a href="https://minorplanetcenter.net/db_search/show_object?utf8=%E2%9C%93&amp;object_id=K21G02T" rel="nofollow noreferrer">2021 GT2</a> is also 3.</p>
<p>In some cases JPL and MPC have different U values for the same asteroid, but the reason isn't obvious to me.</p>
<p><em>Edit</em>: Shortly after the first version of this answer,
a close approach to Earth by 2021 GT2 allowed new observations,
which decreased dT by a factor of 2, dP by a factor of 8, and U by 1.</p>

CC BY-SA 4.0
2022-05-30T09:47:25.077Z
thank you very much for your reply ! I had overlooked the information available for osculating orbital elements in JPL SBDB.
I too have have noted some differences between the U values between JPL and MPC and from what I recall the differences were in the order of 1. I reckon this is probably due to some latest observations/ larger observational arc incorporated into one of these sites, while the other was using non-latest data. However this is only a speculation at this point.
mysterium
CC BY-SA 4.0
2022-05-30T05:01:05.903Z
2022-06-10T15:27:57.417Z
2022-06-10T15:27:57.417Z
Mike G
<p>I'm trying to understand how the orbital <a href="https://minorplanetcenter.net//iau/info/UValue.html" rel="nofollow noreferrer">uncertainty parameter 'U'</a> introduced by the Minor Planet Center (MPC) is actually calculated for minor bodies. <a href="https://en.wikipedia.org/wiki/Uncertainty_parameter" rel="nofollow noreferrer">This Wikipedia page</a> gives the formulae to be used in what appears to be a two-step process of the calculation. The first step involves plugging in a variable referred to as  <span class="math-container">$\Delta \tau$</span>, the uncertainty in the perihelion time in days, to the first formula to obtain what is referred to as the in-orbit longitude runoff, <span class="math-container">$r$</span>.</p>
<p>I'm having trouble finding/ computing <span class="math-container">$\Delta \tau$</span>, the uncertainty in the perihelion time in days for a given minor body. I'm aware that the uncertainties of all the six orbital parameters of a minor body is available at the <a href="https://ssd.jpl.nasa.gov/tools/sbdb_lookup.html#/" rel="nofollow noreferrer">JPL Small Body Database</a>. Does anyone know how to work out the uncertainty in the perihelion time in days from the data available from the JPL Small Body Database?</p>

<asteroids><comets><celestial-mechanics>
calculating MPC orbital uncertainty parameter U
mysterium
# calculating MPC orbital uncertainty parameter U

(Asked by: username_0 on 2022-05-29)

I'm trying to understand how the orbital [uncertainty parameter 'U'](https://minorplanetcenter.net//iau/info/UValue.html) introduced by the Minor Planet Center (MPC) is actually calculated for minor bodies. [This Wikipedia page](https://en.wikipedia.org/wiki/Uncertainty_parameter) gives the formulae to be used in what appears to be a two-step process of the calculation. The first step involves plugging in a variable referred to as $\Delta \tau$, the uncertainty in the perihelion time in days, to the first formula to obtain what is referred to as the in-orbit longitude runoff, $r$.

I'm having trouble finding/ computing $\Delta \tau$, the uncertainty in the perihelion time in days for a given minor body. I'm aware that the uncertainties of all the six orbital parameters of a minor body is available at the [JPL Small Body Database](https://ssd.jpl.nasa.gov/tools/sbdb_lookup.html#/). Does anyone know how to work out the uncertainty in the perihelion time in days from the data available from the JPL Small Body Database?

**Tags:** asteroids, comets, celestial-mechanics

---

## 1 answers

### Answer by username_1 on 2022-05-30. Score: 4 | Accepted answer

Here is a screenshot of JPL SBDB's elements for asteroid 2021 GT2.
The perihelion time tp is shown as a Julian date on the TDB timescale with uncertainty in days.

If I evaluate the MPC formulas:
RUNOFF = (dT * e + 10 / P * dP) * ko / P * 3600 * 3

U = INT(ln(RUNOFF)/CONS)+1  (0 <= U <= 9)

with dT = 0.00022344 d, e = 0.23291, P = 0.93321 y, dP = 0.00028335 d,
ko = 0.98561°, and CONS = 1.4868,
I get RUNOFF = 35.227 and U = 3, matching JPL's "condition code" for this asteroid.
MPC's "uncertainty" for 2021 GT2 is also 3.
In some cases JPL and MPC have different U values for the same asteroid, but the reason isn't obvious to me.
Edit: Shortly after the first version of this answer,
a close approach to Earth by 2021 GT2 allowed new observations,
which decreased dT by a factor of 2, dP by a factor of 8, and U by 1.

> **Comments:**
> **username_0**: thank you very much for your reply ! I had overlooked the information available for osculating orbital elements in JPL SBDB. I too have have noted some differences between the U values between JPL and MPC and from what I recall the differences were in the order of 1. I reckon this is probably due to some latest observations/ larger observational arc incorporated into one of these sites, while the other was using non-latest data. However this is only a speculation at this point.  

---

