Orbital and Escape Velocity Diagram

<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 400 250" width="400" height="250" style="background:#faf9f5;font-family:sans-serif;">
  <!-- Earth -->
  <circle cx="200" cy="125" r="40" fill="#4a90d9" stroke="#2c5f8a" stroke-width="2"/>
  <text x="200" y="129" text-anchor="middle" font-size="12" fill="white" font-weight="bold">Earth</text>
  <text x="200" y="143" text-anchor="middle" font-size="9" fill="white">R = 6400 km</text>

  <!-- Near-surface orbit -->
  <ellipse cx="200" cy="125" rx="65" ry="65" fill="none" stroke="#c6613f" stroke-width="2" stroke-dasharray="5,3"/>
  <text x="275" y="100" font-size="9" fill="#c6613f">Near-surface orbit</text>
  <text x="275" y="112" font-size="9" fill="#c6613f">$v_{0}$ ≈ 7.9 km/s</text>
  <text x="275" y="124" font-size="9" fill="#c6613f">T ≈ 84.6 min</text>

  <!-- Geostationary orbit (scaled down for diagram) -->
  <ellipse cx="200" cy="125" rx="115" ry="115" fill="none" stroke="#788c5d" stroke-width="1.5" stroke-dasharray="8,4"/>
  <text x="320" y="62" font-size="9" fill="#788c5d">Geostationary</text>
  <text x="320" y="74" font-size="9" fill="#788c5d">r ≈ 42,164 km</text>
  <text x="320" y="86" font-size="9" fill="#788c5d">T = 24 h</text>

  <!-- Satellite on near-surface orbit -->
  <circle cx="265" cy="125" r="5" fill="#c6613f"/>
  <text x="268" y="121" font-size="9" fill="#c6613f">Sat.</text>

  <!-- Escape trajectory arrow -->
  <path d="M 230 90 Q 270 50 340 20" stroke="#e74c3c" stroke-width="2" fill="none" marker-end="url(#arrow)"/>
  <text x="290" y="42" font-size="9" fill="#e74c3c">Escape path</text>
  <text x="290" y="54" font-size="9" fill="#e74c3c">vₑ = √2·$v_{0}$</text>

  <!-- Arrow marker -->
  <defs>
    <marker id="arrow" markerWidth="8" markerHeight="8" refX="6" refY="3" orient="auto">
      <path d="M0,0 L0,6 L8,3 z" fill="#e74c3c"/>
    </marker>
  </defs>

  <!-- g field lines -->
  <line x1="200" y1="85" x2="200" y2="68" stroke="#999" stroke-width="1" marker-end="url(#garrow)"/>
  <line x1="240" y1="90" x2="253" y2="76" stroke="#999" stroke-width="1"/>
  <line x1="160" y1="90" x2="147" y2="76" stroke="#999" stroke-width="1"/>
  <defs>
    <marker id="garrow" markerWidth="6" markerHeight="6" refX="5" refY="3" orient="auto">
      <path d="M0,0 L0,6 L6,3 z" fill="#999"/>
    </marker>
  </defs>

  <!-- Labels -->
  <text x="10" y="20" font-size="11" fill="#333" font-weight="bold">Gravitational Orbits — ME-06</text>
  <text x="10" y="240" font-size="9" fill="#888">vₑ = $\sqrt{2GM/R}$ = √2·$v_{0}$; $E_{orbit}$ = −GMm/2r</text>
</svg>

Key Relationships Illustrated

• Inner dashed circle: near-surface orbit ($v_{0}$ ≈ 7.9 km/s)
• Outer dashed circle: geostationary orbit (scaled; real radius ≈ 6.6R)
• Red arrow: escape trajectory (requires v = √2 × $v_{0}$)
• Grey arrows: gravitational field direction (always inward)

Energy Profile from Surface to Infinity