Question
Explain the method to determine distance of a planet from the Earth.
✓
Answer
-
- Parallax method is used to determine distance of different planets from the Earth.
- $E1$ and $E2$ are separated by distance $‘b \ ’$ shown in figure.
$\therefore E1E3 = b$
- The angle between the two directions along which the planet is viewed, can be measured. It is parallax angle, which in this case is $L \angle E1E2 = \theta$
- The planet is far away from the $($Earth$)$ observers, hence
$b << D$
$\therefore \frac{b}{D}<<1$ and ' $\theta$ ' is also very small.
Hence, $E_1 E_2$ can be considered as arc of length $b$ of circle with $S$ as centre and $D$ as radius.
$\therefore E _1 S= E _2 S= D$
$\therefore \theta=\frac{b}{D} \ldots(\theta$ is taken in radian$)$
$\therefore D =\frac{b}{\theta}$
Thus, the distance $'D \ '$ of a far away planet ' $S$ ' can be determined using the parallax method. - The planet should be visible from $E_1$ and $E_2$ observatories simultaneously i.e. at the same time.
- To measure the distance $‘D \ ’$ of a far distant planet $S,$ select two different observatories $(E_1$ and $E_2).$
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