Gravitation — Easy Practice (Set 2)

Quick Recap — Fields, Potential & Satellites

• Variation of $g$: with height $g_h = g\left(1 - \dfrac{2h}{R}\right)$ (for $h\ll R$); with depth $g_d = g\left(1 - \dfrac{d}{R}\right)$.
• Gravitational potential $V = -\dfrac{GM}{r}$ (a scalar); potential energy $U = -\dfrac{GMm}{r}$; both are taken as zero at infinity.
• Orbital velocity $v_o = \sqrt{\dfrac{GM}{r}}$, and $v_e = \sqrt2\, v_o$ at the same radius.
• Satellite energy: total $E = -\dfrac{GMm}{2r}$, with $KE = |E|$ and $PE = 2E$.
• Geostationary satellite: period 24 h, orbiting over the equator at a height of about 36000 km.