1. Determination of the orbit of Didymoon from past and future photometric observations
Petr Scheirich and Petr Pravec
Astronomical Institute AS CR, Ondřejov, Czech Republic
Didymos Observer Workshop
Prague, 2018 June 19

2. Long period component of the lightcurve
2003
2015
2017
2003
2017
2003
2003
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
Past apparitions

3. Didymos orbital model
We modeled the observed mutual events of Didymos using the method of Scheirich and Pravec (2009).
Following function is minimized:
Shapes of the components are approximated with ellipsoids if only lightcurve data are available, or a shape model (e.g., from radar observations) is used.
Main assumptions:
Same albedo of both components
Uniform surface light scattering properties
i = 0 (i.e., there is not present a nodal precession of the mutual orbit)

4. Didymos orbital model Main parameters Diameter ratio
DS/DP = 0.21 ± 0.01
(Scheirich and Pravec 2009)
Eccentricity
e ≤ 0.03
Orbital pole
Lorb, Borb = 270°, -87°
(Scheirich and Pravec 2009, updated using 2015 & 2017 data )
Orbital period
(Porb = ± h)
Assuming zero BYORP!
Allowed (conservative 3-σ uncertainty) area plotted.
Black outline: data
Red outline: data

5. BYORP effect Ćuk & Burns (2005), McMahon & Scheeres (2010a,b)
Binary YORP – shrinking or expanding of the orbit of a synchronous satellite due to the unisotropic reradiation of thermal energy.
The change of semimajor axis  change in mean motion  quadratic rate of change of mean anomaly.

6. BYORP solutions from the 2003-2017 data
DMd (°/yr2) allowed solutions
0.1 (consistent with 0)
-2.3
2.3
3.2
0.9
Prediction (scaled from the 1999 KW4 secondary): 2.8°/yr2
May be any value between -6 and +6°/yr2 perhaps.

7. BYORP solutions from the 2003-2017 data
Five allowed solutions in Porb vs DMd plot.
Porb
DMd
Each period represents different number of cycles between 2003 and 2015.
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
Past apparitions

8. BYORP solutions from the 2003-2017 data
2015
2017
2003
2017
2003
Model lightcurves for the five BYORP solutions.
2003
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
Past apparitions

9. Questions for the next two oppositions (2019, 2021)
Will we be able to determine or constrain the orbital drift by BYORP?
What time distribution and quality of the data will be needed to predict the position of Didymoon with an uncertainty in mean anomaly < 20° at the time of the DART impact in October 2022?
How could additional observations with the HST in Aug-Sep 2020 improve the orbit solution?
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
Past and future apparitions

10. Example of simulated data with RMS residuals of 0.02 mag.
Simulated future apparitions
Properties of simulated data
Cadence:
Mimics the 2017 apparitions
Events covered:
1 – 2 per lunation
RMS residuals:
0.01 or 0.02 mag
Time span:
1 or 3 lunations in each apparition
Assumed DMd:
The five solutions derived from the data.
2003
2017
2003
2019
2003
2019
2021
Example of simulated data with RMS residuals of 0.02 mag.
2015
2017
2021
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
Past and future apparitions

11. Example of simulated data with RMS residuals of 0.01 mag.
Simulated future apparitions
Properties of simulated data
Cadence:
Mimics the 2017 apparitions
Events covered:
1 – 2 per lunation
RMS residuals:
0.01 or 0.02 mag
Time span:
1 or 3 lunations in each apparition
Assumed DMd:
The five solutions derived from the data.
2003
2017
2003
2019
2003
2019
2021
Example of simulated data with RMS residuals of 0.01 mag.
2015
2017
2021
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
Past and future apparitions

12. (#) Depending on actual BYORP value
2019
2021
BYORP resolved from 19&21
Oct M 3σ unc.
HST (RMS 0.02 mag) will help
HST (RMS 0.01 mag) will help
3 lunations
YES
+/-12°
---
YES(!) NO
1 lunation
YES(!$)
YES(#)
+/-9°
RMS 0.02 mag.
RMS 0.01 mag.
(!) Other solutions excluded based on 2015 data (so, not a robust solution)
($) Second BYORP solution excluded based on reliable resolving of events in 2019
(#) Depending on actual BYORP value
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
Past and future apparitions

13. (#) Depending on actual BYORP value
2019
2021
BYORP resolved from 19&21
Oct M 3σ unc.
HST (RMS 0.02 mag) will help
HST (RMS 0.01 mag) will help
3 lunations
YES
+/-12°
---
YES(!) NO
1 lunation
YES(!$)
YES(#)
+/-9°
RMS 0.02 mag.
RMS 0.01 mag.
(!) Other solutions excluded based on 2015 data (so, not a robust solution)
($) Second BYORP solution excluded based on reliable resolving of events in 2019
(#) Depending on actual BYORP value
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
Past and future apparitions

14. Conclusions 2019 2021 BYORP resolved from 19&21 Oct 2022 M 3σ unc.
HST (RMS 0.02 mag) will help
HST (RMS 0.01 mag) will help
3 lunations
YES
+/-12°
--- NO
+/-9°
1 lunation
RMS 0.02
RMS 0.01
Conclusions
Will we be able to determine or constrain the orbital drift by BYORP? Yes.
What time distribution and quality of the data will be needed to predict the position of Didymoon with an uncertainty in mean anomaly < 20° at the time of the DART impact in October 2022? We will need to observe at least 1 event in 1 lunation in 2019 and at least 1 event in each of the 3 lunations in 2021, with photometric rms errors 0.01 mag.
How could additional observations with the HST in Aug-Sep 2020 improve the orbit solution?
Not significantly (assuming the campaign in 2021 is successful).

15. Acknowledgements
Access to computing and storage facilities owned by parties and projects contributing to the National Grid Infrastructure MetaCentrum provided under the programme "Projects of Large Research, Development, and Innovations Infrastructures" (CESNET LM ), is greatly appreciated.