Imagine that Earth did not turn on its axis.

(a) What would be true about the ecliptic?
It would now define the day rather than the year.
It would still be defined and could be seen from all points on Earth, but only when they faced the sun.
It would still be defined, but only from the side of Earth that always faced the sun.
It could no longer be defined.

The ecliptic would remain the path that the sun follows among the stars due to the orbital motion of the earth. You cannot see all of it at once, and some stars along the ecliptic may be invisible duye to sunlight, but they are still there.

In a full year, all parts of the earth would eventually see (face) the sun, unless the Earth is tidally locked to rotate once per year, like the moon is by the earth, once a month.

All parts of the earth would eventually see all of the ecliptic during a year.

None of the choices are correct. Your teacher or homework-question-writer may be of a different opinion, and wrong.

This statement I made is not correct for a nonrotating earth:

"All parts of the earth would eventually see all of the ecliptic during a year."

I still do not agree with any of the choices. The ecliptic will still exist if the earth ceases to rotate. Any place on earth can see some of it, but not all of it, whether facing the sun or not.

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To determine what would be true about the ecliptic if Earth did not turn on its axis, we need to understand what the ecliptic is and how it relates to Earth's rotation.

The ecliptic is the plane of Earth's orbit around the sun. It can be thought of as an imaginary line in space that represents the average path of the sun in the sky throughout the year from Earth's perspective. It is inclined at an angle of about 23.5 degrees relative to Earth's equator.

Currently, Earth's rotation on its axis causes different parts of the planet to face different directions in space as it orbits the sun. This rotation determines the daily cycle of day and night, and it influences the position of the sun in the sky throughout the year.

If Earth did not turn on its axis, there would be significant changes to the daily and yearly patterns we observe. In this scenario:

(a) The correct answer would be: It could no longer be defined.

Without Earth's rotation, the concept of day and night as we know it would cease to exist. The side of Earth that always faced the sun would experience perpetual daylight, while the opposite side would be in constant darkness.

Furthermore, since the ecliptic represents the yearly path of the sun from Earth's perspective, it is tied to Earth's rotation. Without this rotation, the ecliptic would no longer have any relevance or meaning.

Therefore, in the absence of Earth's rotation, the ecliptic could no longer be defined.