Introductory Astronomy Complete University Course - Telescopes: Resolution and Angular Size

A key aspect of telescopes is their angular resolution. Here we discuss what makes up the concept of angular resolution and seeing. This is part of my intro Astronomy class taught at Willam Paterson University and CUNY Hunter. • Telescope’s Resolving Power: The ability of a telescope to discern details of an object, related to its resolution capacity. • Angular Size: How big an object appears to be, dependent on its actual size and distance from the observer. • Tangent and Circles: The tangent of an angle in a circle is a segment of the radius. The adjacent side is the base of the radius, the opposite side is the segment from the base to the circle, and the hypotenuse is the radius itself. • Trigonometry and Right Angles: Trigonometry, which deals with angles and circles, involves right angles. In the context of a circle, the right angle is formed between the opposite and adjacent sides. • Radian Definition: A radian is defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle. • Small Angle Approximation: When angles are very small (measured in arcseconds or arcminutes), the angle in radians can be approximated by the physical size of the object divided by the distance to the object. • Angular Size and Physical Size: The angular size of an object, when very small, can be used to calculate its physical size if the distance to the object is known. • Tangent Approximation: For very small angles measured in radians, the tangent of the angle is approximately equal to the angle itself. • Angular Size Definition: Angular size is how big an object appears to be, influenced by its actual size and distance from the observer. • Telescope Resolving Power: The ability of a telescope to distinguish between two closely spaced objects, such as separating a star from a planet or resolving details within a gas cloud. • Resolving Power of Telescopes: The importance of resolving power in telescopes, which is limited by diffraction of light. • Diffraction and Image Clarity: Explanation of how diffraction, even at the telescope’s aperture, can blur images of distant objects. • Resolution and Detail: Higher resolution allows for clearer images and the ability to distinguish finer details in astronomical objects. • Diffraction Limit: The diffraction of light waves as they pass through an aperture limits the resolution of all telescopes. • Diffraction Pattern: A circular aperture creates a diffraction pattern with a bright central peak and surrounding rings, impacting the clarity of observed objects. • Airy Discs and Telescope Resolution: Airy discs, named after Sir George Airy, are diffraction patterns formed by light entering a telescope’s circular aperture. • Resolving Binary Stars: The ability to distinguish two close stars depends on the separation of their Airy discs. When the first minimum of one Airy disc coincides with the peak of another, the stars reach the diffraction limit. • Diffraction Limit: The diffraction limit is the point at which two point sources of light, such as stars, become indistinguishable from each other when viewed through a telescope. • Rayleigh Criterion Formula: Theta (angular separation) = 1.22 * (wavelength of light) / (diameter of the telescope). • Hubble Space Telescope Example: Using a 2.4m diameter and a wavelength of 500nm, the Hubble Space Telescope has a diffraction limit of about 0.06 arcseconds. • Apollo Mission Flags Visibility: The flags left by the Apollo mission are about four or five feet wide, which is smaller than the Hubble Telescope’s resolution limit, making them invisible to the telescope. • Hubble Space Telescope Limitation: The Hubble Space Telescope’s diameter is insufficient to achieve the desired resolution. • Ground-based Telescope Limitation: Ground-based telescopes, even with a 2-meter diameter, cannot achieve 0.6 arcseconds resolution due to atmospheric turbulence. • Atmospheric Turbulence and “Seeing”: Turbulent air pockets with varying water vapor and temperature refract light, causing the image of stars to wander and resulting in the twinkling effect. • Seeing Definition: Seeing is the spreading of an image on a telescope detector due to the variable refraction of the atmosphere. • Improving Resolution: Building larger telescopes, especially in space to avoid atmospheric interference, is crucial for achieving better angular resolution. 0:00 Introduction 2:21 The Tangent of an angle 5:16 The Definition of the Radian 6:59 Angular Size and Resolving power 9:20 Telescope Size: Resolving power 10:50 Ten Areminute Resolution 11:33 Five Arcsecond Resolution 11:53 One Aresecond Resolution 12:36 Diffraction of Light Waves 13:22 Telescope Diffraction limit: the Rayleigh Criterion 14:44 Telescope Size: the Diffraction Limit. 18:36 Ground-based Telescopes are limited by "Seeing."