Physical Constants
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Introduction
The ScientificConstants package contains values of physical constants. A list of constants can be found here.
Use GetConstant to get the definition of the gravitational constant.
withScientificConstants:
GetConstantg
standard_acceleration_of_gravity,symbol=g,value=9.80665,uncertainty=0,units=ms2
To just return the numerical value,
gravity≔evalfConstant'g'
gravity≔9.80665
Example - Radius of a Geostationary Orbit
The expression for circular orbital velocity around a spherically symmetric body is:
vCircOrb≔G⋅MR:
where, G is the gravitational constant, M is the mass of the body, and R is the radius of orbit.
Now, for geostationary orbit, an orbital velocity of 2 π R meters per day is required, which in meters per second is:
orbitalVelocity≔convert2⋅π⋅R, units, md, ms
orbitalVelocity≔πR43200
Equate this to vCircOrb.
eqn1 ≔ vCircOrb=orbitalVelocity
eqn1≔GMR=πR43200
Solve for R. To disregard the non-real solutions, use the RealDomain package.
use RealDomain inrGeo ≔ solveeqn1, Rend use
rGeo≔720513GM13π23
Replace G with its value and M with the mass of the Earth, then evaluate.
evalfevalrGeo,G=ConstantG, M=ConstantMEarth
4.224068226×107
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