Mapping the stars

Sky map from Stellarium (constellation lines added)

I've heard people ask, if the Earth is spinning and orbiting the sun, then why do people all over the world see the same stars? The answer is that people don't always see the same stars. Here's a few examples:

• People in the southern hemisphere NEVER see Polaris, the North Star.

• People living in Boston never see the Southern Cross (aka Crux), so famous in the southern hemisphere.

• If an amateur astronomer at the North Pole compared night sky observations with an amateur astronomer at the South Pole, they might think they live on different planets. Their sky maps will have no constellations in common.

We know these facts from many decades of observations by professional and amateur astronomers around the world. Here are two examples of time lapse photography of the night sky, one in Arizona and one in Australia.

If you are not familiar with basic astronomy, this post may help you make sense of the above facts. If you are a science teacher, you might consider a nighttime field trip to observe the stars or a trip to a planetarium.

Some nice tools for stargazing

The observations of astronomers have been used to create excellent sky map apps and websites. A good web site is Sky View Cafe. An excellent app is Stellarium, a free open-source planetarium for your computer. The picture above is a screen shot from Stellarium. It allows you to specify your time and place and get various views of the sky; the above view is what you would see lying on the ground in Boston with your feet pointing south and having a fish-eye view of the entire sky. As illustrated by the screenshots below, you can make the ground transparent to reveal the stars below the horizon, and you can dim the sun to see the stars during the day.

Night sky with ground

Same night sky as above with ground removed

Day sky with the sun dimmed to make the stars visible

The celestial sphere

The sun and the stars are too distant for us to have any naked eye depth perception. We can see only their angles, that is, how many degrees a star is above the horizon and how many degrees east of due south. We map the stars on a globe called the celestial sphere. Stars such as those of the Big Dipper are projected onto the surface of this sphere. The Earth is at the center, so when we look at the night sky we are inside the sphere looking out. We can also project much closer objects such as our sun onto the celestial sphere. The poles of the celestial sphere are aligned with the Earth's poles. And we can specify the locations of stars by drawing latitude and longitude lines on the sphere. Astronomers use the respective terms declination and right ascension. The figures and animations below show the exterior of the celestial sphere from a viewpoint that includes a few constellations such as Orion and the Big Dipper.

The celestial sphere

What stars can people see? And when?

There are two reasons why stars may not be visible in a clear sky. First, our fish-eye view of the sky includes only half of the celestial sphere. Which half depends on where we live and when we look. The other half is below our horizon. Second, if the sun is above the horizon, its light illuminates the sky and drowns out the stars. For now, let's switch the sun off and think about what we would see if we had perpetual night.

Visible hemispheres for observer at 42N

The figure above shows an observer living near Boston at time A and about 12 hours later at time B. As the Earth turns, it pans his view of the sky. He never sees the Southern Cross. He always sees the Dipper. He sees Orion only some of the time; it is above his horizon at time A but by time B it has set and is no longer visible. Now let's animate this panning!

Animated celestial sphere

The picture below shows the celestial sphere from a viewpoint that includes a few constellations on the front side.

Celestial sphere. Viewpoint chosen to include particular constellations

Let's show animations of one rotation of the Earth, comparing what I would see in Boston (42N) to what my friend Fabiola would see from her home in Puerto Montt, Chile (41.5S).

The blue region with the yellow stars is the visible hemisphere. First, here's the Boston view:

View of celestial sphere from latitude 42N

You can see Orion rise and set, the Dipper always being above the horizon, and the Southern Cross always being below the horizon. If I watched the northern sky, I would see the Dipper and other northern constellations moving counterclockwise around a point very close to the North Star.

Now let's show what Fabiola sees:

View of celestial sphere from latitude 41.5S

She also sees Orion rise and set. For her, the Southern Cross is always above the horizon, and the Dipper is always below the horizon. If she watched the southern sky, she would see the Cross and other southern constellations moving clockwise around a point in the constellation Octans.

Here comes the sun

Let's now add the sun to the Boston animation. But where should we put the sun on the celestial sphere? It depends on the time of year. Here's a picture showing the Earth's positions in its orbit around the sun at the summer solstice and at the winter solstice. If we could dim the sun enough to see nearby stars in the sky, we'd see the sun close to the constellation Gemini at the summer solstice and close to Sagittarius at the winter solstice. So during the course of the year, the sun appears to move around a great circle on the celestial sphere. This path is known as the ecliptic.

At the summer solstice, the sun and Gemini lie in the same direction.

Here's the Boston animation at the summer solstice, starting from just after sunset. The sun is the orange circle near 10 o'clock:

View of celestial sphere from latitude 42N, now with the sun added

Let's call it a day

How long does it take for the Earth do a 360-degree rotation? Most people would say 24 hours. That's actually wrong. It takes about 23 hours and 56 minutes. This is called the sidereal day, the time it takes for a star to return to the same point in the sky as the previous night. The 24-hour solar day is a bit longer. Why does it take a little longer for the sun to return to the same point in the sky as the previous day? Here's an animation to show what's happening:

One solar day corresponds to 361 degrees of Earth rotation

The dot is a person and the animation goes from one high noon to the next. During that 24-hour period, the Earth progresses about 1 degree in its orbit around the sun. (For clarity, that 1-degree angle is exaggerated in the video.) So, to get the person back to high noon, the Earth has to rotate about 361 degrees. The fact that the solar and sidereal days are not completely in sync is what causes the annual movement of the sun around the celestial sphere.