IB›IB Physics HL›Mind mapsD.1 Gravitational fieldsIB Physics HL: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsKepler, NewtonOrbits are ellipses, Sun at one focusEqual areas in equal times: fastest at perihelionNewton: F=Gm1m2r2F = \frac{Gm_1m_2}{r^2}F=r2Gm1m2, always attractiveCircular orbit: T2r3=4π2GM\frac{T^2}{r^3} = \frac{4\pi^2}{GM}r3T2=GM4π2Field strengthg=Fmg = \frac{F}{m}g=mF, force per unit massSpherical mass: g=GMr2g = \frac{GM}{r^2}g=r2GMField lines radial and inwardsNear surface the field is uniformEnergy, potentialEp=−Gm1m2rE_p = -\frac{Gm_1m_2}{r}Ep=−rGm1m2, zero at infinityVg=−GMrV_g = -\frac{GM}{r}Vg=−rGM, work per unit massPotential is a scalar, so it addsWork done: W=mΔVgW = m\Delta V_gW=mΔVg, path independentGravity fieldsKepler to orbitsgggVgV_gVgGGGGradientg=−ΔVgΔrg = -\frac{\Delta V_g}{\Delta r}g=−ΔrΔVg: negative potential gradientGradient of V against r gives gEquipotentials: no work done along themField lines perpendicular to equipotentialsCloser together where field is strongerOrbitsOrbital speed: v=GMrv = \sqrt{\frac{GM}{r}}v=rGMEscape speed: vesc=2GMrv_{esc} = \sqrt{\frac{2GM}{r}}vesc=r2GMOrbit: Ek=GMm2rE_k = \frac{GMm}{2r}Ek=2rGMm, E=−GMm2rE = -\frac{GMm}{2r}E=−2rGMmDrag lowers orbit and speeds satellite upExam tipsr is centre to centre, not heightmgh only valid where g is constantLarge changes: ΔEp=GMm(1r1−1r2)\Delta E_p = GMm(\frac{1}{r_1} - \frac{1}{r_2})ΔEp=GMm(r11−r21)Drag does not slow a satellite overall