Planetary Satellite Orbiters: Applications for the Moon

<table><svg height="7.1875" id="M187" style="vertical-align:-0.13794pt" version="1.1" viewbox="0 0 7.0749998 7.1875" width="7.0749998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.1875)">
<g transform="translate(72,-66.25)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑒</tspan>
</text>
</g>
</g>
</svg> versus <svg height="9.9250002" id="M188" style="vertical-align:-0.13794pt" version="1.1" viewbox="0 0 4.9875002 9.9250002" width="4.9875002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.925)">
<g transform="translate(72,-64.06)">
<text transform="matrix(1,0,0,-1,-71.95,64.25)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑖</tspan>
</text>
</g>
</g>
</svg>-rad versus <svg height="7.1750002" id="M189" style="vertical-align:-0.1254pt" version="1.1" viewbox="0 0 7.9749999 7.1750002" width="7.9749999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.175)">
<g transform="translate(72,-66.26)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑎</tspan>
</text>
</g>
</g>
</svg>-km. LP165P, Konopliv et al. [<a href="/journals/mpe/2011/187478/#B27">28</a>], <svg height="14.2375" id="M190" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 14.6625 14.2375" width="14.6625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.2375)">
<g transform="translate(72,-60.61)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐽</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.2,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
</text>
</g>
</g>
</svg>–<svg height="14.3875" id="M191" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 14.6625 14.3875" width="14.6625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.3875)">
<g transform="translate(72,-60.49)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐽</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.2,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">5</tspan>
</text>
</g>
</g>
</svg>, <svg height="14.325" id="M192" style="vertical-align:-3.20526pt" version="1.1" viewbox="0 0 14.6625 14.325" width="14.6625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.325)">
<g transform="translate(72,-60.54)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐽</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.2,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">7</tspan>
</text>
</g>
</g>
</svg>. Green color is the surface when <svg height="13.6125" id="M193" style="vertical-align:-2.34499pt" version="1.1" viewbox="0 0 56.674999 13.6125" width="56.674999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.6125)">
<g transform="translate(72,-61.11)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑔</tspan>
<tspan style="font-size: 12.50px; " x="9.6148071" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.655195" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="27.906696" y="0">𝜋</tspan>
<tspan style="font-size: 12.50px; " x="35.508518" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="38.984352" y="0">2</tspan>
</text>
</g>
</g>
</svg>, and the red is obtained for <svg height="13.6125" id="M194" style="vertical-align:-2.34499pt" version="1.1" viewbox="0 0 48.862499 13.6125" width="48.862499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.6125)">
<g transform="translate(72,-61.11)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑔</tspan>
<tspan style="font-size: 12.50px; " x="9.6148071" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.655195" y="0">𝜋</tspan>
<tspan style="font-size: 12.50px; " x="29.257021" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="32.732853" y="0">2</tspan>
</text>
</g>
</g>
</svg>.</table>

Mathematical Problems in Engineering

Planetary Satellite Orbiters: Applications for the Moon

Figure 3