parallax shift for the star when observed from Earth, this particular parallax shift is often called the star's annual parallax . See the diagram below. Clearly, then, by using a right-angled triangle, as shown above, the angle p is known, as is the length of the side opposite this angle -- the radius of the Earth's orbit. Therefore the distance d to the nearby star can be calculated using trigonometry as follows: sin p = radius of Earth's orbit / d Since, the angle p is very small, we can use the approximation sin q = tan q = q for q small, and hence we have that the distance, d , in parsecs, to the nearby star is given by: where p = parallax angle (annular parallax) of the star in arcseconds. Clearly, the larger a star's annual parallax, the closer the star is to Earth. Note also that for objects within our own Solar System, it is possible to use trigonometric parallax, with the diameter of the Earth as the baseline to calculate distances to these objects. For such an object, observations of the object are made 12 hours apart to obtain the diurnal (or geocentric) parallax angle and then a similar procedure to that described above is used to determine the distance to the object. EXERCISE: Barnard's star has a parallax angle of 0.545 arcsec. Determine the distance from Earth to the star. (1.83 pc) Limitations of Trigonometric Parallax Measurements Measuring parallax angles from the ground is