~Introduction

A.M.E. invented by Dr. Ayesha Mansour, who began research into planets’ magical effect
-Studied at Cambridge University
-There are ways to calculate factors that determine the amount of light that a non-luminous celestial body reflects towards the Earth
-Need to know amount of sunlight celestial body receives from sun, which is dependednt on sunlight production. Distance from sun affects amount of sunlight the body gets

~Distance From Sun

-amount of light an object receives from Sun varies with inverse(decreases with increasing distance) of the square of its distance from the Sun
-the farther a body is from the Sun, the less of the Sun’s light it gets.
-Uranus is about twice as far from the Sun as Saturn, so it gets about a quarter less sunlight than Saturn

~Angular Size

-Size of object as seen by an observer on Earth
-Not physical measurement; it's angular separation between 2 ends of object
-The bigger the angular size of object, the more light it sends to Earth
-the amount of light it sends increases with the angular area of the object, but this depends on the square of the angular size.

~Albedo

-Derived from Latin word 'Albus' meaning white
-ratio of the light reflected off the surface to that incident hitting the surface
-Surface reflecting no light is 0
-Surface reflecting all light is 1
-Albedo of any surface is in the middle
-Dry sand albedo: 0.4, or 40% of reflected light
-Fresh snow albedo: 0.9, or 90%
-Charcoal albedo: 0.05, or 5%
-Substance with highest known albedo: magnesium oxide, which is 0.96 or 96%
-Substance with lowest known albedo: Black velvet, which is 0.01-0.03, or 1%-3%

~Phase

-Phase of non-luminous celestial body is between 0 and 1
-The more of the body is lit, the more light it sends to earth
-Sun lights half of the body facing it
-Phases range from new(almost none lit) to full(almost all lit)
-Moon is not only body with phases: Mercury and Venus also have them
-Proportion of body that is lit can be either blocked by another body or if part of the body is blocked by the shadow of another body
-Phase: proportion of a body that's lit and can be seen from earth
-4 quantities(albedo, distance from Sun, angular size, phase) are independent of each other
-Albedo of moon does not depend on phase
-New moon reflects as much light as full moon; the light just doesn't reach earth
-Angular size depends on albedo's distance from earth

~Formula For the Amount of Light Reflected to Earth

-(Angular size)^2 *albedo*phase/(distance from sun)^2
-In words,
angular size squared, times albedo, times phase, divided by distance from sun squared

~Dr. Mansour's Contribution

--Magical Albedo vs. Optical Albedo

-Dr. Mansour modified formula to accommodate magic
-light-colored objects generally reflect more magic than dark-colored
-There are exceptions(Ex: Light can't pass through clouds and walls easily but magic can)
-Some metals absorb light, and some metals and stone absorb magic
-Magical albedo of a non-luminous celestial body: ratio of the magic reflected from the body to that incident hitting the body.
-Magic reflected by various bodies interact with each other

--Interference

-Only component of A.M.E. unique to magic
-magic is influenced by magic reflected off of other bodies in the sky
-2 Types: constructive and destructive
-Constructive interference: occurs when reflections from 2+ magical sources enhance each other so that the magic reflected from each of those objects is stronger than it would be normally(TOTAL constructive interference is when the reflected magic from 1 of the bodies is doubled)
-Destructive interference: occurs when reflections from 2+ magical sources partly or fully cancel each other out so there's less or no magic emitting from either(TOTAL destructive interference is when there's a complete cancellation of a body's magic)
-Objects that appear to be 90 degrees apart don't interfere with each other
-Objects closer than 90 degrees apart interfere constructively(the closer, the more constructive)
-Objects farther than 90 degrees apart interfere destructively(the farther, the more destructive)
-The more magic a body reflects toward earth, the less it's interfered with
-Interference ranges from -1 to 1, and a 1 is added to the A.M.E. equation
-Total constructive/destructive interference can't be achieved
-Full moon's magic is so strong that it can almost do so to other bodies
-Jupiter tends to increase the power of spells/other magic, and Mars tends to make people more likely to commit violence

~Putting It All Together

-Final equation:
(angular size)^2*magical albedo*phase/(distance from sun)^2 * (interference+1)
-In words,
angular size squared, times magical albedo, times phase, divided by distance from sun squared, all times interference plus one

~Assignments

-Mandatory quiz(A.M.E. in depth)
-Midterm!