Editing Apsis (section)

== Time of perihelion ==
[[Orbital elements]] such as the ''time of perihelion passage'' are defined at the [[Epoch (astronomy)|epoch]] chosen using an unperturbed [[Two-body problem|two-body solution]] that does not account for the [[n-body problem]]. To get an accurate time of perihelion passage you need to use an epoch close to the perihelion passage. For example, using an epoch of 1996, [[Comet Hale–Bopp]] shows perihelion on 1 April 1997.<ref>{{Cite web |url=https://ssd.jpl.nasa.gov/sbdb.cgi?soln=J971A%2F1&sstr=Hale-Bopp&cad=1 |title=JPL SBDB: Hale-Bopp (Epoch 1996) |access-date=July 16, 2020 |archive-date=July 16, 2020 |archive-url=https://web.archive.org/web/20200716170854/https://ssd.jpl.nasa.gov/sbdb.cgi?soln=J971A%2F1&sstr=Hale-Bopp&cad=1 |url-status=live }}</ref> Using an epoch of 2008 shows a less accurate perihelion date of 30 March 1997.<ref>{{Cite web |url=https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=1995O1 |title=JPL SBDB: Hale-Bopp |access-date=July 16, 2020 |archive-date=July 17, 2020 |archive-url=https://web.archive.org/web/20200717063814/https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=1995O1 |url-status=live }}</ref> [[Short-period comet]]s can be even more sensitive to the epoch selected. Using an epoch of 2005 shows [[101P/Chernykh]] coming to perihelion on 25 December 2005,<ref>{{Cite web |url=http://www.oaa.gr.jp/~oaacs/nk/nk1293.htm |title=101P/Chernykh – A (NK 1293) by Syuichi Nakano |access-date=July 17, 2020 |archive-date=October 3, 2020 |archive-url=https://web.archive.org/web/20201003194829/http://www.oaa.gr.jp/~oaacs/nk/nk1293.htm |url-status=live }}</ref> but using an epoch of 2012 produces a less accurate unperturbed perihelion date of 20 January 2006.<ref>[https://web.archive.org/web/20201128092431/https://ssd.jpl.nasa.gov/sbdb.cgi?ID=c00101_0 JPL SBDB: 101P/Chernykh (Epoch 2012)]</ref>

{{anchor|12P}}
{| class="wikitable sortable" style="text-align: center; font-size: 0.9em;"
|+[[Two-body problem|Two body]] solution vs [[n-body problem|n-body]] solution for [[12P/Pons–Brooks]] time of perihelion passage
! [[Epoch (astronomy)|Epoch]]
! [[#Time of perihelion|Date of perihelion (tp)]]
|-
| [https://archive.today/20220623124113/https://ssd.jpl.nasa.gov/tools/sbdb_lookup.html%23/?sstr=12P&view=OPC 2010] || 2024-Apr-19.892
|-
| [[n-body problem|n-body]]<ref name="Horizons2024">{{cite web
  |title=Horizons Batch for 12P/Pons-Brooks (90000223) at 2024-Apr-21 03:20
  |publisher=[[JPL Horizons On-Line Ephemeris System|JPL Horizons]]
  |type=Perihelion occurs when rdot flips from negative to positive
  |url=https://ssd.jpl.nasa.gov/horizons_batch.cgi?batch=1&COMMAND=%2790000223%27&START_TIME=%272024-Apr-21%2003:00%27&STOP_TIME=%272024-Apr-21%2003:40%27&STEP_SIZE=%27120%27&QUANTITIES=%2719%27
  |archive-url=https://web.archive.org/web/20230212102447/https://ssd.jpl.nasa.gov/horizons_batch.cgi?batch=1&COMMAND=%2790000223%27&START_TIME=%272024-Apr-21%2003:00%27&STOP_TIME=%272024-Apr-21%2003:40%27&STEP_SIZE=%27120%27&QUANTITIES=%2719%27
  |archive-date=2023-02-12
  |url-status=live
  |access-date=2023-02-11}} (JPL#K242/3 Soln.date: 2022-Oct-24)</ref> || 2024-Apr-21.139
|-
| [https://archive.today/20230211111847/https://ssd.jpl.nasa.gov/tools/sbdb_lookup.html%23/?sstr=12P&view=OPC 2018] || 2024-Apr-23.069
|}

[[Numerical integration]] shows [[dwarf planet]] [[Eris (dwarf planet)|Eris]] will come to perihelion around December 2257.<ref name="Eris">{{cite web
  |title = Horizons Batch for Eris at perihelion around 7 December 2257 ±2 weeks
  |type = Perihelion occurs when rdot flips from negative to positive. The JPL SBDB generically (incorrectly) lists an unperturbed two-body perihelion date in 2260
  |url = https://ssd.jpl.nasa.gov/horizons_batch.cgi?batch=1&COMMAND=%27Eris%27&START_TIME=%272257-11-28%27&STOP_TIME=%272257-12-17%27&STEP_SIZE=%273%20hours%27&QUANTITIES=%2719%27
  |work = [[JPL Horizons On-Line Ephemeris System|JPL Horizons]]
  |publisher = Jet Propulsion Laboratory
  |access-date = 13 September 2021
  |archive-date = September 13, 2021
  |archive-url = https://web.archive.org/web/20210913110143/https://ssd.jpl.nasa.gov/horizons_batch.cgi?batch=1&COMMAND=%27Eris%27&START_TIME=%272257-11-28%27&STOP_TIME=%272257-12-17%27&STEP_SIZE=%273%20hours%27&QUANTITIES=%2719%27
  |url-status = live
  }}</ref> Using an epoch of 2021, which is 236 years early, less accurately shows Eris coming to perihelion in 2260.<ref>{{Cite web |url=https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=Eris |title=JPL SBDB: Eris (Epoch 2021) |access-date=January 5, 2021 |archive-date=January 31, 2018 |archive-url=https://web.archive.org/web/20180131234951/https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=Eris |url-status=live }}</ref>

[[4 Vesta]] came to perihelion on 26 December 2021,<ref name="Horizons2021">{{cite web
  |title=Horizons Batch for 4 Vesta on 2021-Dec-26
  |publisher=[[JPL Horizons On-Line Ephemeris System|JPL Horizons]]
  |type=Perihelion occurs when rdot flips from negative to positive
  |url=https://ssd.jpl.nasa.gov/horizons_batch.cgi?batch=1&COMMAND=%27Vesta%27&START_TIME=%272021-Dec-25%2023:00%27&STOP_TIME=%272021-Dec-26%2004:00%27&STEP_SIZE=%2715%20minutes%27&QUANTITIES=%2719%27
  |access-date=2021-09-26
  |archive-date=September 26, 2021
  |archive-url=https://web.archive.org/web/20210926095954/https://ssd.jpl.nasa.gov/horizons_batch.cgi?batch=1&COMMAND=%27Vesta%27&START_TIME=%272021-Dec-25%2023%3A00%27&STOP_TIME=%272021-Dec-26%2004%3A00%27&STEP_SIZE=%2715%20minutes%27&QUANTITIES=%2719%27
  |url-status=live
  }} (Epoch 2021-Jul-01/Soln.date: 2021-Apr-13)</ref> but using a two-body solution at an epoch of July 2021 less accurately shows Vesta came to perihelion on 25 December 2021.<ref>[https://web.archive.org/web/20210926095422/https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=4 JPL SBDB: 4 Vesta (Epoch 2021)]</ref>

===Short arcs===
[[Trans-Neptunian object]]s discovered when 80+ AU from the Sun need dozens of observations over multiple years to well constrain their orbits because they move very slowly against the background stars. Due to statistics of small numbers, trans-Neptunian objects such as {{mpl|2015 TH|367}} when it had only 8 observations over an [[observation arc]] of 1 year that have not or will not come to perihelion for roughly 100 years can have a [[68–95–99.7 rule|1-sigma]] uncertainty of {{Convert|28220|day|year|order=flip|abbr=off}} in the perihelion date.<ref>{{Cite web |url=https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=2015TH367 |title=JPL SBDB: 2015 TH367 |access-date=September 23, 2021 |archive-date=March 14, 2018 |archive-url=https://web.archive.org/web/20180314133928/https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=2015TH367 |url-status=bot: unknown }}</ref>