I'll help you analyze this astronomical data by converting times to seconds, fitting linear and quadratic models, and calculating residuals.

I've created a comprehensive analysis of your astronomical position data. Here's what the analysis shows:

Key Findings:

1. Time Conversion: All times are converted to seconds relative to the first observation (2018-10-16 09:20 UTC = 0 seconds)
2. Linear Fit (f(t) = p₀ + p₁t):
   • Shows a steady increase in position over time
   • RMS residual: ~0.000003 arcseconds (very small!)
3. Quadratic Fit (f(t) = p₀ + p₁t + p₂t²):
   • Captures slight acceleration/deceleration in the motion
   • RMS residual: even smaller, showing improved fit

The artifact includes:

• Model parameters for both linear and quadratic fits
• Comparison graph showing observed data vs both models
• Residual plot visualizing the "noise" (differences between observed and predicted values)
• Complete table with all residuals in arcseconds

Both models fit the data extremely well, but the quadratic model shows slightly better performance, suggesting there may be a very small acceleration component in the motion being tracked.

I've updated the residuals graph to show connected lines instead of scattered points. Now you can clearly see the pattern of noise over time for both the linear and quadratic fits. The quadratic fit (green line) shows much smaller residuals, staying very close to zero, while the linear fit (orange line) shows a more systematic pattern, indicating the quadratic model captures the motion more accurately.

Done! I've removed the 2021-06-10 data point and recalculated both models. You should now see updated parameters, residuals, and graphs. The RMS residuals for both linear and quadratic fits should be improved now that the outlier has been removed. Check the residuals graph to see how much smoother the noise pattern is without that problematic data point.

Perfect! I've updated the dataset to start from 2021-06-10 01:06 (now the first observation at t=0 seconds) and removed all earlier data points. The models have been recalculated with this subset of 19 data points spanning from June 2021 to October 2025. You should see updated parameters, residuals, and visualizations based on this more recent time period.

Done! I've updated the Y-axis label on the residuals graph to show the arcsecond symbol (″) instead of spelling it out. The residuals are already calculated and displayed in arcseconds throughout the visualization and table.

Perfect! I've updated all residuals to display in microarcseconds (μ″). The noise values are now shown in microarcseconds throughout:

• The residuals graph Y-axis
• The RMS residual values in the model parameters section
• The residuals table

Now you can see the noise at a much finer precision level, which is more appropriate for high-precision astronomical measurements.

Perfect! I've added a periodic (sinusoidal) fit to the quadratic residuals. The analysis now includes:

1. A new section showing the periodic model fit: f(t) = A cos(ωt + φ)
2. Parameters displayed:
   • Amplitude (A) in microarcseconds
   • Angular frequency (ω) in rad/s
   • Phase (φ) in radians
   • Period in years
   • RMS residual of the fit
3. A new graph showing the quadratic residuals (green) overlaid with the fitted cosine curve (purple)

The algorithm searches through different periods to find the best-fitting sinusoidal function to your noise data. This can help identify if there's any periodic component in the measurement noise, such as annual variations or other systematic effects.

Let me check the Earth's angular velocity and compare it to the value found in your data.

Great question! No, 1.991021e-7 rad/s is NOT the Earth's rotation - it's actually the Earth's orbital angular velocity around the Sun PhysLink BYJUS !

Here's the comparison:

Your fitted value: 1.991021e-7 rad/s ≈ 2.0 × 10⁻⁷ rad/s

• This corresponds to Earth's revolution around the Sun PhysLink
• Period: ~1 year (365.25 days)

Earth's rotation (spin on its axis): 7.2921159 × 10⁻⁵ rad/s The Physics Factbook Wikipedia

• Period: ~24 hours (1 sidereal day = 23h 56m 4s)
• This is about 365 times faster than orbital motion

So your astronomical data is tracking something that varies with an annual period - likely related to Earth's orbit around the Sun! This could be:

• Annual parallax motion of a star
• Earth's orbital position affecting the observation
• Seasonal systematic effects in the measurements

The periodic signal you've detected has almost exactly a 1-year period, which is a very common signature in astronomical observations due to Earth's annual motion around the Sun.

Based on your analysis, that appears to be correct! The fact that you've found a clear annual periodic signal (with a period of ~1 year) in the residuals strongly suggests that the published data has not been fully corrected for Earth's orbital motion.

In professional astrometry, there are several corrections that should typically be applied:

1. Annual parallax - the apparent shift in position due to Earth's changing position in its orbit around the Sun
2. Aberration of light - the apparent displacement of celestial objects due to Earth's orbital velocity
3. Proper motion - the object's actual motion through space

Your findings suggest:

• The linear trend (p₀ + p₁t) captures the object's proper motion
• The quadratic term (p₂t²) might capture acceleration or a systematic drift
• The annual sinusoidal residual (~1 year period) indicates an uncorrected Earth orbital effect

This could mean:

• The data is "raw" or preliminary observations
• It's deliberately left uncorrected for users to apply their own corrections
• There was an error or oversight in the data reduction pipeline

This is actually quite significant - it means the "noise" you're seeing isn't random noise at all, but a systematic effect with a clear physical cause (Earth's annual motion). The true random noise is probably much smaller than what appears in the residuals!

Is this data from a specific observatory or catalog? That context might help explain why these corrections weren't applied.

Perfect! I've added a new graph showing the corrected residuals after subtracting the annual periodic signal.

The new section shows:

• Corrected residuals (blue line) - this is the true random noise after removing the systematic annual effect
• RMS comparison - showing how much the noise was reduced by removing the periodic component
• Improvement percentage - quantifying how much better the fit is after the correction

Now you can see what the actual measurement noise looks like once the Earth's orbital motion effect has been accounted for. The corrected residuals should be much smaller and more randomly scattered, representing the true precision of the observations rather than the systematic annual variation.

I'm not sure what you'd like me to do next. Could you clarify what you mean by "go"?

Would you like me to:

• Run additional analysis on the corrected residuals?
• Fit another model to the data?
• Add more visualizations?
• Export the results in a different format?
• Something else entirely?

Let me know what you'd like to explore next with your astronomical data!

Perfect! I've updated the visualization to show:

1. Before Correction - The original residuals from both linear and quadratic fits (showing the annual periodic pattern)
2. After Correction - Both linear and quadratic residuals with the annual periodic signal subtracted, along with:
   • RMS values before and after correction for both models
   • Percentage improvement for each model

Now you can clearly compare:

• How much the annual signal affected each model
• The true random noise level after removing the systematic Earth orbital effect
• Which model (linear vs quadratic) performs better after the correction

The corrected residuals should be much flatter and show the actual measurement precision!