IB›IB Physics SL›Mind mapsD.1 Gravitational fieldsIB Physics SL: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsKepler's lawsOrbits are ellipses, Sun at one focusEqual areas in equal timesFastest at perihelion, slowest at aphelionT2∝r3T^2 \propto r^3T2∝r3 for the same central massCircular orbit: T2r3=4π2GM\frac{T^2}{r^3} = \frac{4\pi^2}{GM}r3T2=GM4π2Newton's lawF=Gm1m2r2F = \frac{Gm_1m_2}{r^2}F=r2Gm1m2Always attractive, equal and oppositeInverse-square: double r, force ÷ 4G=6.67×10−11 N m2kg−2G = 6.67 \times 10^{-11}\,\text{N m}^2\text{kg}^{-2}G=6.67×10−11N m2kg−2Point massesSpherical body acts as mass at its centreOr size tiny compared with separationIrregular bodies up close are not point massesGravitygravitational fieldsgggGGGN/kgField strengthg=F/mg = F/mg=F/m, force per unit massg=GMr2g = \frac{GM}{r^2}g=r2GM for a spherical massA vector pointing towards the massUnits: N kg⁻¹ = m s⁻²Orbiting astronauts are in free fallField linesShow force direction on a test massRadial and inwards for a sphereCloser lines mean stronger fieldNear surface: parallel, nearly uniformLines never crossExam tipsr is centre to centre, add the radiusWeightless does not mean g = 0Kepler III compares same central mass only