MaplePortal/PhysicalConstants - Maple Help

 Physical Constants

 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.

 > $\mathrm{with}\left(\mathrm{ScientificConstants}\right):$
 > $\mathrm{GetConstant}\left(g\right)$
 ${\mathrm{standard_acceleration_of_gravity}}{,}{\mathrm{symbol}}{=}{g}{,}{\mathrm{value}}{=}{9.80665}{,}{\mathrm{uncertainty}}{=}{0}{,}{\mathrm{units}}{=}\frac{{m}}{{{s}}^{{2}}}$ (1)

To just return the numerical value,

 > $\mathrm{gravity}≔\mathrm{evalf}\left(\mathrm{Constant}\left('g'\right)\right)$
 ${\mathrm{gravity}}{≔}{9.80665}$ (2)

 Example - Radius of a Geostationary Orbit

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

 > ${v}_{\mathrm{CircOrb}}≔\sqrt{\frac{G\cdot M}{R}}:$

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:

 >
 ${\mathrm{orbitalVelocity}}{≔}\frac{{\mathrm{\pi }}{}{R}}{{43200}}$ (3)

Equate this to ${v}_{\mathrm{CircOrb}}$.

 >
 ${\mathrm{eqn1}}{≔}\sqrt{\frac{{G}{}{M}}{{R}}}{=}\frac{{\mathrm{\pi }}{}{R}}{{43200}}$ (4)

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

 >
 ${{r}}_{{\mathrm{Geo}}}{≔}\frac{{720}{}{{5}}^{{1}}{{3}}}{}{\left({G}{}{M}\right)}^{{1}}{{3}}}}{{{\mathrm{\pi }}}^{{2}}{{3}}}}$ (5)

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

 >
 ${4.223324010}{}{{10}}^{{7}}$ (6)