I try to understand this code and I actually understood the whole thing except these 2 line:
f_grav = gravity * sun.mass * earth.mass * (sun.pos - earth.pos).norm() / (sun.pos - earth.pos).mag2
earth.vel = earth.vel + (f_grav/earth.mass) * dt
Why couldn't it just be: f_grav = gravity * sun.mass * earth.mass / (sun.pos-earth.pos)**2
I also dont get the role of .norm() and .mag2
Here is the whole code snippet of the program(GlowScript):
sunRadius = 10 * realSunRadius # the size for our solar system
earthRadius = sunRadius * 0.25 # note: real value would be sunRadius * 0.01, a good choice for sim is * 0.25
astronomicalUnit = 212.7 * realSunRadius # the distance from Sun to Earth - the Sun is about 100 Sun diameters away
gravity = 6.6e-11 # sets the strength of the gravitational constant to 6.6x10-11 Newton x meters squared per kilograms squared
# create the Sun object
sun = sphere( radius = sunRadius, opacity = 0.7, emissive = True, texture = "http://i.imgur.com/yoEzbtg.jpg" )
sun.mass = 2e30 # mass of the Sun in kilograms is 2,000,000,000,000,000,000,000,000,000,000 kg
sun.pos = vec(0,0,0)
sun.vel = vec(0,0,0)
# place a few sources of light at the same position as the Sun to illuminate the Earth and Moon objects
sunlight = local_light( pos = vec(0,0,0), color=color.white )
more_sunlight = local_light( pos = vec(0,0,0), color=color.white ) # I found adding two lights was about right
# create the Earth object
earth = sphere ( radius = earthRadius, texture = "http://i.imgur.com/rhFu01b.jpg",make_trail=True)
earth.mass = 6e24 # mass of Earth in kilograms
earth.pos = vec(astronomicalUnit, 0, 0)
earth.vel = vec(0,0,-30000) # the Earth is moving around 30000 m/s
dt = 10000
# below is the main loop of the program - everything above is "setup" and now we are in the main "loop" where all the action occurs
while (True): # this will make it loop forever
rate(100) # this limits the animation rate so that it won't depend on computer/browser processor speed
# calculate the force of gravity on each object
f_grav = gravity * sun.mass * earth.mass * (sun.pos - earth.pos).norm() / (sun.pos - earth.pos).mag2
earth.vel = earth.vel + (f_grav/earth.mass) * dt
# update the position of the Earth and Moon by using simple circle trigonometry
earth.pos = earth.pos + earth.vel * dt
(sun.pos-earth.pos) is a vector. I don't think you can do (sun.pos-earth.pos)**2 because you can't square a vector. Unless you're trying to do a dot product of the vector with itself? But the result of a dot product is a scalar, so f_grav would be a scalar. Forces are vectors, so it doesn't make sense to use a dot product there.
In comparison, f_grav = gravity * sun.mass * earth.mass * (sun.pos - earth.pos).norm() / (sun.pos - earth.pos).mag2 makes sense because you're multiplying (sun.pos - earth.pos).norm(), a vector, by three scalars, and dividing by one scalar. So the result is a vector as desired.