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- How to work out the formula relating the number of sidereal vs the number of solar days for a generic planet orbit.

Hi all,

I've a doubt about the following formula for the number of sidereal vs solar days for a generic planet orbit (e.g. the Earth's orbit around the Sun):

$$N_{sid} = N_{sol} + 1$$

Section 1.5 of the book "Foundation of Astrophysics" - B. Ryden shows how to calculate the above equation starting from the angular velocity ##\vec \omega_{sid}## of the Earth's rotation in the non-rotating sidereal frame where "fixed starts" are at rest and the angular velocity ##\vec \omega_{E}## of the Earth's orbital motion in the same sidereal frame.

$$\vec \omega_{sid} (t) = \vec \omega_{sol} (t) + \vec \omega_{E} (t)$$

##\vec \omega_{sol} (t)## is the angular velocity of the Earth's rotation in a reference frame that co-rotates with the Earth-Sun line.

As far as I can understand ##\vec \omega_{sid} (t)## actually represents the

Is that correct ? Thanks you.

I've a doubt about the following formula for the number of sidereal vs solar days for a generic planet orbit (e.g. the Earth's orbit around the Sun):

$$N_{sid} = N_{sol} + 1$$

Section 1.5 of the book "Foundation of Astrophysics" - B. Ryden shows how to calculate the above equation starting from the angular velocity ##\vec \omega_{sid}## of the Earth's rotation in the non-rotating sidereal frame where "fixed starts" are at rest and the angular velocity ##\vec \omega_{E}## of the Earth's orbital motion in the same sidereal frame.

$$\vec \omega_{sid} (t) = \vec \omega_{sol} (t) + \vec \omega_{E} (t)$$

##\vec \omega_{sol} (t)## is the angular velocity of the Earth's rotation in a reference frame that co-rotates with the Earth-Sun line.

As far as I can understand ##\vec \omega_{sid} (t)## actually represents the

*whole*Earth's angular velocity that include all the 'rotation components', not just the angular velocity of the Earth spinning around its North-South axis.Is that correct ? Thanks you.

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