Cast a Long Shadow

Previously, I shared a post about a conversation with my son about the rising sun viewed at different latitudes. During that conversation, we also discussed how the length of our shadow varied over the course of a year. In winter at noon in the northern hemisphere, when the sun is low in the sky, our shadows are cast long to the north. In summer, our shadows are shorter due to the higher angle of the sun in the sky.

Imagine a plane extending through the earth at the equator. Extend that equatorial plane out into space. Between late March and late September, the sun appears above that plane. It reaches its highest extent in late June at the summer solstice. The sun appears at the elevation of the plane on the equinoxes in late March and late September. It appears at its farthest extent below the equatorial plane in late December at the winter solstice. The farthest north and south of the equatorial plane reached by the sun is 23.5˚.

Normal Shadows

Melanie and I live about 42˚ north of the equator. In the summer months, the sunlight direction is above the equatorial plane several degrees. Our short shadows are cast to the north at noon. In the winter months, the sunlight direction is below the equatorial plane. Our shadows are cast longer to the north. The blue man in this figure is not to scale, but illustrates the concept of casting of shadows.

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Morning Sun

I explained to my son how my shadow was cast almost straight down at noon when we were 12˚south of the equator in Peru. That had never happened to me before. Living 42˚north of the equator, we always cast shadows. They are short in the summer when the Sun is high in the sky and long in the winter when the Sun is low. But, never straight down like this.

My son posed a question about sunrises at the equator. “Does the Sun rise straight up due east each day of the year.” I said it doesn’t rise due east every day. But, it does rise nearly straight up. He acted skeptical. It was time to use desktop planetarium software to simulate the view.

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