Explain the method for the measurement of the diameter of a planet or star.
(N/A) Angular diameter: The angle subtended by the diameter of a planet or star at a point on the surface of the Earth is called the angular diameter $(\alpha)$.
Let the diameter of the planet be $d$ and the distance between the Earth and the planet be $D$.
As shown in the figure,from a point of observation on the surface of the Earth,the angle $\alpha$ is subtended by the diameter $d$ of the planet.
Since the distance $D$ is very large compared to the diameter $d$,we can use the relation:
$\alpha = \frac{d}{D}$ (where $\alpha$ is in radians).
Therefore,the diameter of the planet is given by:
$d = \alpha D$
This formula is used to measure the diameter $(d)$ of the planet.
Conversion factors:
$1^{\circ} = 60^{\prime} (\text{minutes})$
$1^{\prime} = 60^{\prime \prime} (\text{seconds})$
$1^{\circ} = 3600^{\prime \prime} (\text{seconds})$
Let the diameter of the planet be $d$ and the distance between the Earth and the planet be $D$.
As shown in the figure,from a point of observation on the surface of the Earth,the angle $\alpha$ is subtended by the diameter $d$ of the planet.
Since the distance $D$ is very large compared to the diameter $d$,we can use the relation:
$\alpha = \frac{d}{D}$ (where $\alpha$ is in radians).
Therefore,the diameter of the planet is given by:
$d = \alpha D$
This formula is used to measure the diameter $(d)$ of the planet.
Conversion factors:
$1^{\circ} = 60^{\prime} (\text{minutes})$
$1^{\prime} = 60^{\prime \prime} (\text{seconds})$
$1^{\circ} = 3600^{\prime \prime} (\text{seconds})$
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