This can be proven mathematically fairly easily, at least on a sphere and neglecting refraction. The algorithm can also be followed in Google Earth Pro with the "circle ruler" tool.

Let us denote your location $Y$ (without loss of generality we assume it is in the northern hemisphere). Then we define the subsolar point $S$, the point on the surface of the Earth where the Sun is directly overhead. This is obviously unique at any moment in time and its latitude is equal to the current solar declination $\delta$. We only need to show that the direction towards the subsolar point is north of east for any sunrise in summer and south of east for any sunrise in winter.

You can see the Sun rising or setting if and only if the subsolar point is exactly 90° away, or about 10000 km on the surface. This set of points is, by definition, a great circle, and we'll call it $g$.

Unless you are at one of the poles, $g$ intersects the equator at two distinct points, and they must be antipodes (exactly on the opposite sides of the Earth). We'll name them $A$ and $B$, with $A$ being the one to the east and $B$ to the west.

Now draw a plane $ABY$ through these two points and your location. The angle between the equatorial plane and the plane $ABY$ is equal to your geographic latitude, and your location is the northernmost point of its intersection with the surface. Therefore, your line of sight $\vec{YA}$ points exactly east and $\vec{YB}$ points exactly west.

Finally, as we have shown, for any sunrise at any time of the year, the subsolar point must lie on circle $g$, and its latitude must be $\delta$. So if

• $\delta > 0$ (northern spring or summer), the subsolar point is in the northern hemisphere, and you see the rising Sun left of $A$, or further north than east, and its azimuth is $< 90°$,
• and if $\delta < 0$ (northern autumn or winter), the subsolar point is in the southern hemisphere, and the rising Sun is right of $A$, or further south than east, and its azimuth is $> 90°$.

This can be proven mathematically fairly easily, at least on a sphere and neglecting refraction. The algorithm can also be followed in Google Earth Pro with the "circle ruler" tool.

Let us denote your location $Y$ (without loss of generality we assume it is in the northern hemisphere). Then we define the subsolar point $S$, the point on the surface of the Earth where the Sun is directly overhead. This is obviously unique at any moment in time and its latitude is equal to the current solar declination $\delta$. We only need to show that the direction towards the subsolar point is north of east for any sunrise in summer and south of east for any sunrise in winter.

You can see the Sun rising or setting if and only if the subsolar point is exactly 90° away, or about 10000 km on the surface. This set of points is, by definition, a great circle, and we'll call it $g$.

Unless you are at one of the poles, $g$ intersects the equator at two distinct points, and they must be antipodes (exactly on the opposite sides of the Earth). We'll name them $A$ and $B$, with $A$ being the one to the east and $B$ to the west.

Now draw a plane $ABY$ through these two points and your location. The angle between the equatorial plane and the plane $ABY$ is equal to your geographic latitude, and your location is the northernmost point of its intersection with the surface. Therefore, your line of sight $\vec{YA}$ points exactly east and $\vec{YB}$ points exactly west.

Finally, as we have shown, for any sunrise at any time of the year, the subsolar point must lie on circle $g$, and its latitude must be $\delta$. So if

• $\delta > 0$ (northern spring or summer), the subsolar point is in the northern hemisphere, and you see the rising Sun left of $A$, or further north than east, and its azimuth is $< 90°$,
• and if $\delta < 0$ (northern autumn or winter), the subsolar point is in the southern hemisphere, and the rising Sun is right of $A$, or further south than east, and its azimuth is $> 90°$.

The whole situation depicted for a random place $Y$ (Warsaw to be honest). Green line $\vec{YA}$ points directly east, the direction of sunrise on equinox. The orange one points to the northernmost sunrise ($\delta = +\varepsilon \approx 23.44$, at summer solstice) and the blue one to the southernmost one ($\delta = -\varepsilon \approx -23.44°$, at winter solstice).

This can be proven mathematically fairly easily, at least on a sphere and neglecting refraction. The algorithm can also be followed in Google Earth Pro with the "circle ruler" tool.

Let us denote your location $Y$ (without loss of generality we assume it is in the northern hemisphere). Then we define the subsolar point $S$, the point on the surface of the Earth where the Sun is directly overhead. This is obviously unique at any moment in time and its latitude is equal to the current solar declination $\delta$. We only need to show that the direction towards the subsolar point is north of east for any sunrise in summer and south of east for any sunrise in winter.

You can see the Sun rising or setting if and only if the subsolar point is exactly 90° away, or about 10000 km on the surface. This set of points is, by definition, a great circle, and we'll call it $g$.

Unless you are at one of the poles, $g$ intersects the equator at two distinct points, and they must be antipodes (exactly on the opposite sides of the Earth). We'll name them $A$ and $B$, with $A$ being the one to the east and $B$ to the west.

Now draw a plane $ABY$ through these two points and your location. The angle between the equatorial plane and the plane $ABY$ is equal to your geographic latitude and your location is its northernmost point. Therefore on the surface $\vec{YA}$ points exactly east and $\vec{YB}$ points exactly west.

Finally, as we have shown, for any sunrise at any time of the year, the subsolar point must be at some point on the circle $g$, and its latitude must be $\delta$. So if

• $\delta > 0$ (northern spring or summer), the subsolar point is in the northern hemisphere, and you see the rising Sun left of $A$, or further north than east, and its azimuth is $< 90°$,
• and if $\delta < 0$ (northern autumn or winter), the subsolar point is in the southern hemisphere, and the rising Sun is right of $A$, or further south than east, and its azimuth is $> 90°$.

This can be proven mathematically fairly easily, at least on a sphere and neglecting refraction. The algorithm can also be followed in Google Earth Pro with the "circle ruler" tool.

Let us denote your location $Y$ (without loss of generality we assume it is in the northern hemisphere). Then we define the subsolar point $S$, the point on the surface of the Earth where the Sun is directly overhead. This is obviously unique at any moment in time and its latitude is equal to the current solar declination $\delta$. We only need to show that the direction towards the subsolar point is north of east for any sunrise in summer and south of east for any sunrise in winter.

You can see the Sun rising or setting if and only if the subsolar point is exactly 90° away, or about 10000 km on the surface. This set of points is, by definition, a great circle, and we'll call it $g$.

Unless you are at one of the poles, $g$ intersects the equator at two distinct points, and they must be antipodes (exactly on the opposite sides of the Earth). We'll name them $A$ and $B$, with $A$ being the one to the east and $B$ to the west.

Now draw a plane $ABY$ through these two points and your location. The angle between the equatorial plane and the plane $ABY$ is equal to your geographic latitude, and your location is the northernmost point of its intersection with the surface. Therefore, your line of sight $\vec{YA}$ points exactly east and $\vec{YB}$ points exactly west.

Finally, as we have shown, for any sunrise at any time of the year, the subsolar point must lie on circle $g$, and its latitude must be $\delta$. So if

• $\delta > 0$ (northern spring or summer), the subsolar point is in the northern hemisphere, and you see the rising Sun left of $A$, or further north than east, and its azimuth is $< 90°$,
• and if $\delta < 0$ (northern autumn or winter), the subsolar point is in the southern hemisphere, and the rising Sun is right of $A$, or further south than east, and its azimuth is $> 90°$.