Astronomical Observation

All astronomical objects, be they galaxies, stars or planets, appear differently to observers in different places. Objects appear larger and brighter the closer an observer is to the object. Small objects (such as the moon) may appear larger than anything else in the sky due to their proximity, while the largest of galaxies may be invisible to the naked eye or blocked by relatively nearby objects.

How a civilisation views astronomical objects may have an enormous impact on their culture and way of thinking, and thus it is an important thing to consider.

Stars
We can determine the intensity of a star’s light as perceived on any given point in the solar system (and beyond). Given the luminosity of the star and the distance from the star to the observer, we can calculate the apparent brightness of a star as :



The answer, when converted to actual values, is in W/m2.

Planets
Determining the brightness of planets is not as easy as determining the brightness of stars, as planets do not radiate light as stars do, but rather reflect it. A measure of a planet's ability to reflect light is called its bond albedo: a value which ranges from 0 to 1. A planet with an albedo of 0 absorbs all light (and hence is pure black), and a planet with an albedo of 1 reflects all light (and hence is pure white). Below are the bond albedos of some solar system bodies. The apparent brightness of any planet P, orbiting a star S, as observed from an observer O is given by:



Where a is P's bond albedo, LS is S's luminosity (in watts), RP is the radius of P (in metres), DPS is the distance between P and S (in metres) and DOP is the distance between O and P (in metres). The answer will be in W/m2.

Apparent Size
We can calculate how big an object will appear, based on the small-angle approximation. Given the radius of the object and the distance between the object and the observer, we can calculate its apparent size (relative to the Sun) as:



Where 1 θ☉ is the apparent size of the Sun from Earth, which is roughly 0.5°. The moon has roughly the same apparent size from Earth.

Comparing the apparent size of the object to the apparent size of other nearby objects (notably moons), we can determine whether or not total eclipses are possible.

We can also use the apparent size to determine whether or not the object in question can be seen with the naked eye. As a rule of thumb, anything smaller than 0.01145916° can not be seen by the naked human eye.