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Assume the present epoch has the same age as present-day Jupiter, the host now has solar luminosity, and moving inward did not change the stipulated intrinsic cooling law or its normalization. This neglects persistent tidal heating and irradiation-induced suppression of cooling. The intrinsic planetary luminosity is then approximately $L_{\mathrm{int},\mathrm{J}}$, not its value at the migration epoch.

Define incident irradiation as intercepted power before reflection,Comparing with present-day Jupiter at $a_J\simeq 5\mathrm{AU}$ givesFor equal radii,Retaining unequal radii multiplies the right side by $(R_J/R_p{)}^2$. If irradiation instead denotes incident radiative flux per area, the orbital factor is still $10^4$, but it must be compared with an intrinsic flux consistently. Absorbed power also includes $1-A_B$, so comparisons of absorbed irradiation require the two Bond albedos.

Close-in gas giants motivate planetary migration when compared with formation models. Two useful observational diagnostics are then orbital eccentricities and spin-orbit geometry. An eccentric population of wider potential progenitors together with circular short-period orbits supports eccentricity excitation followed by tidal dissipation. The second diagnostic is stellar obliquity, including misaligned or retrograde orbits measured through the Rossiter-McLaughlin effect; these can favour scattering or secular pathways over smooth coplanar migration. Conversely, aligned resonant architectures are compatible with disc-driven migration. None is unique: primordial disc tilt or alternative formation can mimic some signatures. The expected present-day ratio is suppressed by the inverse-square orbital factor, while eccentricities and spin-orbit geometry test migration pathways.

Planetary migration changes a planet's orbital semimajor axis through torques from a disc or exchanges of energy and angular momentum with other bodies, often followed by tidal dissipation. Short-period giant planets, eccentric progenitors, resonant architectures, and stellar obliquity provide complementary constraints rather than one unique migration diagnostic.

A transiting body hides different velocity regions of a rotating stellar disc and causes an anomalous measured Doppler shift. Its time dependence constrains the sky-projected spin-orbit angle, which is not generally the full stellar obliquity.