A tangent line to a circle is a line that touches the circle at exactly one point – Wikipedia

Fig #1: when the earth rotates on its axis but has zero orbital motion.

Tangent A touches C exactly at x or Anti-Noon x

Tangent B touches C exactly at y or Noon y

A common point of C and tangent A is x

A common point of C and tangent B is y

Noon and Midnight are happening in this case INSTANTLY.

Fig #2: When the earth rotates on its axis and has also orbital motion

As said

Tangent A touches C exactly at x or Anti-Noon x

Tangent B touches C exactly at y or Noon y - Similarly,

Tangent A1 touches C exactly at x1 or Anti-Noon x1

Tangent B1 touches C exactly at y1 or Noon y1

Tangent A2 touches C exactly at x2 or Anti-Noon x2

Tangent B2 touches C exactly at y2 or Noon y2

Tangent A3 touches C exactly at x3 or Anti-Noon x3

Tangent B3 touches C exactly at y3 or Noon y3 .... and son on

When there is a midnight x , there is a noon y and hence

When there is midnight x1,, there is a is noon y1

When there is midnight x2,, there is a is noon y2

When there is midnight x3,, there is a is noon y3 and so on

Original Diagram of the question

The outer circle is traced by all the Midnights (x, x1, x2, x3……) on earth in space due to the spin of earth on axis and its orbital motion

The inner circle is traced by all the Middays (y, y1, y2, y3……) on earth in space due to the spin of earth on axis and its orbital motion

If both Noons and Midnights were instant and equal in numbers then, the

Circumference of outer circle must be equal to the Circumference of inner circle but

Circumference of outer circle > Circumference of inner circle and hence

# of Midnights > # of Middays or

Occurrence of midnights > Occurrence of middays

Since the instantaneous

Orbital velocity of Point x > Orbital velocity of Point y

Orbital velocity of Point x1 > Orbital velocity of Point y1

Orbital velocity of Point x2 > Orbital velocity of Point y2

Orbital velocity of Point x3 > Orbital velocity of Point y3 and so on

Therefore, the

Drag of Point x > Drag of Point y in space

Drag of Point x1 > Drag of Point y1 in space

Drag of Point x2 > Drag of Point y2 in space

Drag of Point x3 > Drag of Point y3 in space and so on

The earth spins on its axis at the speed of 30 m/sec.

The travelling speed of earth is 30,000 m/sec in its orbit.

As 30,000 m/sec >>>> 30 m/sec , therefore either # of Midnights > # of Middays (which is impossible)

or there must be the happening of drag of midday and midnight in the orbit of earth if the

Circumference of outer circle > Circumference of an inner circle

I called this Drag or gentle ride of midnight (or midday) in space DURATION between the happening of x and x1 (or y and y1)

Although the orbital speed of midnight > middays but the DURATION between the two successive midnights (say x1 and x2) is same and = DURATION between the two successive middays (say y1 and y2)

Shadow growth stops (or very very slow) due to the gentle ride or transferring of noon or midnight to next point on earth during this DURATION