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--- courses:ast201:4 [2023/11/05 01:07] – [4.2 Radial velocity] asad
+++ courses:ast201:4 [2023/11/08 21:10] (current) – [2.1 Astronomical Unit (AU)] asad
@@ Line 124: / Line 124: @@
 where $\Delta t$ is the time it takes for a radio signal to come back to earth after getting reflected from Venus.
-==== - Stellar parallax ====
+==== - Distance ladder ====
-{{:courses:ast201:parallactic-ellipse.png?nolink&700|}}
+{{:uv:distance-ladder.webp?nolink&600|}}
-{{ :courses:ast201:parallax-angle.png?nolink&150|}}
-The tangent of the parallactic angle
-$$ \tan p = \frac{a}{r} $$
-where $r$ is the distance to the object and $a$ is in au. For $p\ll 1$ we can approximate $\tan p = \sin p = p$ and
-$$ p = \frac{a}{r}. $$
-If $a$ is in au and $p$ in arcsec, then $r$ is in parsec.
-parsec = 206265 au = $3.085678\times 10^{16}$ m = 3.261633 ly.
-{{:courses:ast201:plate-measuring-machine.png?nolink|}}
-For nearby star, measurements of $p$ have uncertainties of 50 mas, but can be reduced to 5 mas. Only works for around 1000 stars closer than 20 pc.
-HIPPARCOS has parallax uncertainties of 0.97 mas for around 118k stars brighter than $m_V=8.0$.
-Explore Gaia: https://www.esa.int/Science_Exploration/Space_Science/Gaia
 ===== - Time =====
 TAI: International Atomic Time defines 1 SI second as 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperﬁne levels of the ground state of the cesium-133 atom. Practical atomic clocks have a precision of about $2/10^{13}$. Two clocks located at two frames will have differing speed based on their relative velocities (special relativity) and their accelerations or local gravitational fields (general relativity).