Timing and phase

15 chapters, each an animated explainer with its physics and sources. Every drawing says whether it is an illustration, a model from stored values, or real data, and by how much it is exaggerated. Only the transit chapter is something SetuHQ itself does.

Chapter 8 of 15

Timing and phase

A transit is one moment in an orbit. The rest of the orbit carries information too: when transits arrive, how the planet glows as it turns, when it slips behind its star, and which half of the spinning star it covers.

Illustration
Four scenes. Transit timing: two planets near a 2:1 period ratio tug each other, so the inner planet's transits arrive early and late and an O−C diagram builds up. Secondary eclipse: the planet slips behind its star half an orbit after transit, a much smaller dip, drawn ten times deeper. Phase curve: a tidally locked planet shows more of its hot day side towards occultation, with its peak shifted by winds. Rossiter–McLaughlin: the planet covers the approaching and then the receding half of the rotating star, so the star's measured velocity swings during transit.

The numbers

QuantityValueFrom
Kepler-9 b and c periods19.23891 d and 38.9853 dexoplanet.eu; near 2:1, so their transits shift by minutes per orbit (Holman et al. 2010)
TRAPPIST-1 b eclipse at 15 µm, measured861 ± 99 ppmJWST MIRI (Greene et al. 2023); dayside 503 K, as expected for bare rock
Same, blackbody star and planet606 ppmδ ≈ k² B(503 K)/B(2560 K) at 15 µm, k from exoplanet.eu radii [calc]; real analyses use a stellar model spectrum, not a blackbody
HD 189733 b hot-spot offset16 ± 6° before oppositionSpitzer 8 µm phase curve (Knutson et al. 2007)
Rossiter–McLaughlin, HD 189733 b86 m/sK_R ≈ V sin I · k² with V sin I = 3.5 km/s and k = 0.157, both from Gaudi & Winn 2007 Table 1, which lists 88 m/s [calc]
Rossiter–McLaughlin, HD 189733 b (measured V sin I)83 m/sV sin I = 3.316 +0.017/−0.067 km/s and k = 0.15812, measured by Triaud et al. 2009 (Table 2) [calc]
Rossiter–McLaughlin, HD 209458 b69 m/sV sin I = 4.7 km/s, k = 0.121 (Gaudi & Winn 2007 list 70 m/s) [calc]

SetuHQ measures each dip's time and checks the odd and even dips against each other; it does not fit timing variations, phase curves or eclipses. The secondary-eclipse depth on the canvas is drawn ten times deeper and says so; the TTV amplitude is illustrative. Spin–orbit angles span aligned, polar and retrograde orbits (Albrecht et al. 2022).

Planets in this chapterKepler-9 b ›Kepler-9 c ›HD 189733 Ab ›HD 209458 b ›
Sources

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