Since it is easy to measure the angular size of astronomical objects, we often use this to solve for other unknowns, such as the distance or the diameter of a celestial body. If two objects are roughly the same distance from the observer, you can also use the formula to find the distance between the two objects.

Since one radian equals 3600⋄(180/π) ≈ 206265 arcseconds, we can then rewrite this as the Small Angle Formula: where θ is now measured in arcseconds, d is the physical size or separation, and D is the distance to the object.

The distance between degrees of longitude has great variation because they are farthest apart at the equator and coverage at the poles. 1. A degree of longitude is widest at the equator with a distance of 69.172 miles or 111.321 Km. The distance between a degree of longitude at 40° north or south is 53 miles or 85 Km.

The small-angle approximation is the term for the following estimates of the basic trigonometric functions, valid when θ ≈ 0 : /theta /approx 0: θ≈0: sin ⁡ θ ≈ θ , cos ⁡ θ ≈ 1 − θ 2 2 ≈ 1 , tan ⁡ θ ≈ θ .

We can generate another simple formula: Angular size in degrees = (size * 57.29) / distance No doubt you can figure out the formulas for minutes and seconds of arc.

Angular Size is measured in arcminutes and arcseconds, which are used to represent angles on a sphere. An arcsecond is 1/3600th of one degree, and a radian is 180/π degrees, so one radian equals 3,600*180/π arcseconds, which is about 206,265 arcseconds.

Jupiter

The angular size of an object is determined uniquely by its actual size and its distance from the observer. For an object of fixed size, the larger the distance, the smaller the angular size. For objects at a fixed distance, the larger the actual size of an object, the larger its angular size.

A 1 cm object at 1 m produces the same size of final image on the retina as a 10 cm object at 10 m. This is why the “angular size” q of an object viewed by eye is often an important quantity. Imaging by an eyeball. The angle subtended by the object determines the linear size of the final image on the retina.

To figure out the image size, just follow these simple steps:

1. Multiply the width and height of the image, in pixels, to get the total pixel count.
2. Multiply the total pixel count by 3 to get the image size in bytes.
3. Divide the number of bytes by 1024 to get the image size in kilobytes.

The relationship is a simple inverse, i.e. If you keep the same object and the same focal length you get: size = 1/ distance (the =-sign should be proportional-sign).

A pop-up window will open with the dimensions of your image displaying in the More Info section. The dimensions show the pixel height and width of your photo. On a PC, right click on the image file, look at Properties, and then view the Summary tab.