Definition of Stellar Parallax from Alonso and Finn Volume 1

[vibha_ganji]

Hi! I read this definition of Stellar Parallax "It is expressed quantitatively by one-half the angle subtended by the Earth's diameter E1E2 perpendicular to the line joining the star and the sun (see Fig. 2-10)." (Source Alonso and Finn: Volume 1). But, I was unable to understand how they derived this definition. Is there some typo or am I misuderstanding the description? Here is Figure 2-10. (This is not a homework question but rather a doubt I had when I was reading.)

 

[mathman]

A definition is just that. It is not derived. You need to clarify your concern.

 

[vibha_ganji]

Sorry about that. What I meant was I do not understand how the definition represents the angle theta. When the text writes, “ It is expressed quantitatively by one-half the angle subtended by the Earth's diameter E1E2 perpendicular to the line joining the star and the sun,” do they mean the angle subtended by the Earth’s orbit’s diameter and the line perpendicular to the line joining the star and the sun or do they mean the Earth’s diameter itself?

 

[Drakkith]

Pretty sure they mean the Earth's orbit's diameter. Hence why they say E1E2.
The diameter of the Earth doesn't make much sense by being here since the parallax is due almost entirely to Earth's orbit.