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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

(1)

To just return the numerical value,

gravityevalfConstant'g'

gravity9.80665

(2)

 

Example - Radius of a Geostationary Orbit

 

The expression for circular orbital velocity around a spherically symmetric body is:

 

vCircOrbGMR:

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:

orbitalVelocityconvert2πR, units, md, ms

orbitalVelocityπR43200

(3)

Equate this to vCircOrb.

eqn1  vCircOrb=orbitalVelocity

eqn1GMR=πR43200

(4)

 

Solve for R. To disregard the non-real solutions, use the RealDomain package.

use RealDomain inrGeo  solveeqn1, Rend use

rGeo720513GM13π23

(5)

Replace G with its value and M with the mass of the Earth, then evaluate.

 

evalfevalrGeo,G=ConstantG, M=ConstantMEarth

4.223324010107

(6)