When is a star highest in the sky? Looking at the diagram on the right, it is clear that a star reaches its highest point in the sky when it crosses the observer's meridian, the line which passes through the zenith and the south point on the horizon.
As we discussed previously, for stars which rise and set, the star is said to transit when it crosses this line. Thus, the highest point a star reaches in the sky is known as it's transit altitude. The diagram below shows how to calculate the transit altitude for a star of declination δ, for an observer at latitude Φ.
As shown here, the north celestial pole lies at an altitude of Φ above the horizon, and the celestial equator is 90° away. At it's highest point, the celestial equator attains an altitude of 90-Φ, as shown above. The declination of the star is measured from the celestial equator, and so the transit altitude of our star is given by 90-Φ+δ. The star will be due south when it transits. What about a star in the direction given by the red arrow? For this star, the formula 90-Φ+δ yields an altitude of more than 90°, but as we have seen, altitude ranges from 0° to 90°. Instead, we must use the formula 180-(90-Φ+δ), as shown in the diagram below. This star will be due north when it transits.
The animation below allows you to explore the transit altitude of stars from anywhere on the Earth's surface; it might also help you visualise how the horizon diagrams above are obtained. Click on the steps in turn to draw in the Celestial poles, equator and star's position. Drag the celestial sphere around to get a 3-D view, or click 'side-view' to see how the 3-D celestial sphere relates to the horizon diagrams above.