transit
Definition: Transit denotes the physical quantity, process, or inference concept captured by this lecture-specific statement: For a planet of radius Rp transiting a star of radius Rstar, the fractional decrease in observed flux at mid-transit (ignoring stellar limb darkening) is the ratio of blocked area to total area: delta = (Rp/Rstar)^2, a purely geometric relation independent of the planet’s mass or...
Why it matters here: Lecture 01’s radial-velocity method gives a planet’s mass (times sin i) but says nothing about its size. The transit method, derived here, supplies the missing radius -- and, combined with radial velocity for the same planet, breaks the sin(i) degeneracy exactly and yields the planet’s true mass, true radius, and therefore its...
Relationships: It is used with transit depth to interpret the lecture model. The quantitative connection is the working relation \(\delta = \left(\dfrac{R_p}{R_\ast}\right)^{2}, \qquad T_{\rm dur} \approx \dfrac{P}{\pi}\arcsin\!\left(\dfrac{R_\ast}{a}\right)\).
Boundary or common confusion: Assuming transit depth alone gives a planet’s absolute size. Transit depth only ever gives the ratio Rp/Rstar; converting to an absolute planet radius requires an independently known stellar radius (from the star’s spectral type, parallax-based luminosity, or asteroseismology), so an error in the assumed stellar radius propagates directly and proportionally...
transit depth
Definition: Transit depth denotes the physical quantity, process, or inference concept captured by this lecture-specific statement: Computed transit depth delta = (Rp/Rstar)^2 = 1.30%, matching the discovery team’s measured 1.5% dip to within the precision of the adopted stellar radius.
Why it matters here: Lecture 01’s radial-velocity method gives a planet’s mass (times sin i) but says nothing about its size. The transit method, derived here, supplies the missing radius -- and, combined with radial velocity for the same planet, breaks the sin(i) degeneracy exactly and yields the planet’s true mass, true radius, and therefore its...
Relationships: It is used with transit, transit duration to interpret the lecture model. The quantitative connection is the working relation \(\delta = \left(\dfrac{R_p}{R_\ast}\right)^{2}, \qquad T_{\rm dur} \approx \dfrac{P}{\pi}\arcsin\!\left(\dfrac{R_\ast}{a}\right)\).
Boundary or common confusion: Assuming transit depth alone gives a planet’s absolute size. Transit depth only ever gives the ratio Rp/Rstar; converting to an absolute planet radius requires an independently known stellar radius (from the star’s spectral type, parallax-based luminosity, or asteroseismology), so an error in the assumed stellar radius propagates directly and proportionally...
transit duration
Definition: Transit duration denotes the physical quantity, process, or inference concept captured by this lecture-specific statement: For a central (impact parameter b=0), circular-orbit transit, the total transit duration is approximately T = (P/pi) * arcsin(Rstar/a), because the star subtends an angular half-width of arcsin(Rstar/a) as seen from the planet’s orbital position; more precise treatments add ingress/egress...
Why it matters here: Lecture 01’s radial-velocity method gives a planet’s mass (times sin i) but says nothing about its size. The transit method, derived here, supplies the missing radius -- and, combined with radial velocity for the same planet, breaks the sin(i) degeneracy exactly and yields the planet’s true mass, true radius, and therefore its...
Relationships: It is used with transit depth, ingress/egress to interpret the lecture model. The quantitative connection is the working relation \(\delta = \left(\dfrac{R_p}{R_\ast}\right)^{2}, \qquad T_{\rm dur} \approx \dfrac{P}{\pi}\arcsin\!\left(\dfrac{R_\ast}{a}\right)\).
Boundary or common confusion: Assuming transit depth alone gives a planet’s absolute size. Transit depth only ever gives the ratio Rp/Rstar; converting to an absolute planet radius requires an independently known stellar radius (from the star’s spectral type, parallax-based luminosity, or asteroseismology), so an error in the assumed stellar radius propagates directly and proportionally...
ingress/egress
Definition: Ingress/egress denotes the physical quantity, process, or inference concept captured by this lecture-specific statement: For a central (impact parameter b=0), circular-orbit transit, the total transit duration is approximately T = (P/pi) * arcsin(Rstar/a), because the star subtends an angular half-width of arcsin(Rstar/a) as seen from the planet’s orbital position; more precise treatments add ingress/egress...
Why it matters here: Lecture 01’s radial-velocity method gives a planet’s mass (times sin i) but says nothing about its size. The transit method, derived here, supplies the missing radius -- and, combined with radial velocity for the same planet, breaks the sin(i) degeneracy exactly and yields the planet’s true mass, true radius, and therefore its...
Relationships: It is used with transit duration, impact parameter to interpret the lecture model. The quantitative connection is the working relation \(\delta = \left(\dfrac{R_p}{R_\ast}\right)^{2}, \qquad T_{\rm dur} \approx \dfrac{P}{\pi}\arcsin\!\left(\dfrac{R_\ast}{a}\right)\).
Boundary or common confusion: Assuming transit depth alone gives a planet’s absolute size. Transit depth only ever gives the ratio Rp/Rstar; converting to an absolute planet radius requires an independently known stellar radius (from the star’s spectral type, parallax-based luminosity, or asteroseismology), so an error in the assumed stellar radius propagates directly and proportionally...
impact parameter
Definition: Impact parameter denotes the physical quantity, process, or inference concept captured by this lecture-specific statement: For a central (impact parameter b=0), circular-orbit transit, the total transit duration is approximately T = (P/pi) * arcsin(Rstar/a), because the star subtends an angular half-width of arcsin(Rstar/a) as seen from the planet’s orbital position; more precise treatments add ingress/egress...
Why it matters here: Lecture 01’s radial-velocity method gives a planet’s mass (times sin i) but says nothing about its size. The transit method, derived here, supplies the missing radius -- and, combined with radial velocity for the same planet, breaks the sin(i) degeneracy exactly and yields the planet’s true mass, true radius, and therefore its...
Relationships: It is used with ingress/egress, occultation (secondary eclipse) to interpret the lecture model. The quantitative connection is the working relation \(\delta = \left(\dfrac{R_p}{R_\ast}\right)^{2}, \qquad T_{\rm dur} \approx \dfrac{P}{\pi}\arcsin\!\left(\dfrac{R_\ast}{a}\right)\).
Boundary or common confusion: Assuming transit depth alone gives a planet’s absolute size. Transit depth only ever gives the ratio Rp/Rstar; converting to an absolute planet radius requires an independently known stellar radius (from the star’s spectral type, parallax-based luminosity, or asteroseismology), so an error in the assumed stellar radius propagates directly and proportionally...
occultation (secondary eclipse)
Definition: Occultation (secondary eclipse) denotes the physical quantity, process, or inference concept captured by this lecture-specific statement: For a planet of radius Rp transiting a star of radius Rstar, the fractional decrease in observed flux at mid-transit (ignoring stellar limb darkening) is the ratio of blocked area to total area: delta = (Rp/Rstar)^2, a purely geometric relation independent of the planet’s mass or...
Why it matters here: Lecture 01’s radial-velocity method gives a planet’s mass (times sin i) but says nothing about its size. The transit method, derived here, supplies the missing radius -- and, combined with radial velocity for the same planet, breaks the sin(i) degeneracy exactly and yields the planet’s true mass, true radius, and therefore its...
Relationships: It is used with impact parameter to interpret the lecture model. The quantitative connection is the working relation \(\delta = \left(\dfrac{R_p}{R_\ast}\right)^{2}, \qquad T_{\rm dur} \approx \dfrac{P}{\pi}\arcsin\!\left(\dfrac{R_\ast}{a}\right)\).
Boundary or common confusion: Assuming transit depth alone gives a planet’s absolute size. Transit depth only ever gives the ratio Rp/Rstar; converting to an absolute planet radius requires an independently known stellar radius (from the star’s spectral type, parallax-based luminosity, or asteroseismology), so an error in the assumed stellar radius propagates directly and proportionally...