If we know the distance d to an object we are observing, we can then use it with the angular size θ and the Small Angle Formula to find the physical size D of that celestial object.

For small angles, the trigonometric functions sine, cosine, and tangent can be calculated with reasonable accuracy by the following simple approximations: provided the angle is measured …

(R) Separation distance between the two objects.

When the angle θ (in radians) is small we can use these approximations for Sine, Cosine and Tangent: If we are very daring we can use cos θ ≈ 1. Let's see some values! (Note: values are …

Some objects in the sky have an apparent size - like the moon. By understanding geometry and the nature of circles, it is possible to determine the distance to the object, or the physical …

The small angle formula, or small-angle approximation, states that for very small angles measured in radians, the sine and tangent of the angle are approximately equal to the angle itself (sin θ ≈ …

Feb 4, 1998 · Both formulas only work for small angles. If you use this formula and get a big angle (more than about 10 degrees), it will not be accurate and would need to be calculated by more …

Very handy and powerful formula If angular diameter and distance known =&#062 linear diameter how sizes of planets and Sun determined If angular diameter and distance known =&#062 …

4 days ago · Small oscillations of a simple pendulum are best modeled using the small-angle approximation. The small oscillations of a simple pendulum are a basic example in mechanics …

The figure below shows a graphical representation of the small-angle approximation for the sin (θ) function. You can see the linear function θ and the trigonometric function sin (θ) closely match …