At what height is g = g/9?

At what depth is g = 3g/4?

A planet has mass 8M_E and radius 2R_E. Its escape velocity compared to Earth's is:

Two satellites have orbital radii r and 4r. The ratio of their periods is:

A satellite in circular orbit fires engines forward briefly. The orbit becomes: <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 300 280" style="max-width:300px;margin:0.5em auto;display:block;"> <title>Satellite fires engines forward — orbit becomes elliptical</title> <rect width="300" height="280" fill="#faf9f5" rx="6"/> <defs><marker id="ah-q17s2" markerWidth="8" markerHeight="6" refX="8" refY="3" orient="auto"><polygon points="0 0, 8 3, 0 6" fill="#c6613f"/></marker></defs> <!-- Earth --> <circle cx="150" cy="140" r="25" fill="#e8e0d4" stroke="#14140f" stroke-width="1.5"/> <text x="150" y="144" text-anchor="middle" font-size="8" font-family="sans-serif" fill="#14140f">Earth</text> <!-- Original circular orbit (dashed) --> <circle cx="150" cy="140" r="70" fill="none" stroke="#14140f" stroke-width="1" stroke-dasharray="4,3"/> <!-- Elliptical orbit after burn --> <ellipse cx="170" cy="140" rx="100" ry="80" fill="none" stroke="#c6613f" stroke-width="1.5"/> <!-- Burn point (perigee of new orbit) --> <circle cx="80" cy="140" r="5" fill="#c6613f"/> <text x="55" y="135" font-size="8" font-family="sans-serif" fill="#c6613f">burn</text> <text x="45" y="147" font-size="7" font-family="sans-serif" fill="#c6613f">(perigee)</text> <!-- Velocity arrow at burn --> <line x1="80" y1="135" x2="80" y2="100" stroke="#c6613f" stroke-width="2" marker-end="url(#ah-q17s2)"/> <text x="63" y="110" font-size="8" font-family="sans-serif" fill="#c6613f">v + $\Delta v$</text> <!-- Apogee --> <circle cx="270" cy="140" r="3" fill="#788c5d"/> <text x="270" y="130" text-anchor="middle" font-size="7" font-family="sans-serif" fill="#788c5d">apogee</text> <!-- Labels --> <text x="200" y="265" font-size="8" font-family="sans-serif" fill="#14140f">— — original (circular)</text> <text x="200" y="250" font-size="8" font-family="sans-serif" fill="#c6613f">——— new (elliptical)</text> </svg>