Derive Keplers 3rd law
Equate gravitational force (GMm/r^2) to centripetal force (mv^2/r). Rearrange to get v^2=GM/r. Due to the approximated circular orbit v=2pir/T so v^2=4pi^2r^2/T^2. Therefore GM/r=4pi^2r^2/T^2. Rearranging gives GM=4pi^2r^3/T^2. Rearranging futher gets T^2=(4pi^2/GM)r^3. Hence T^2 is proportional to r^3.
MS
Related Physics A Level answers
All answers ▸A projectile is fired out of a cannon at 50 km/s, at an angle of 30 degrees and an elevation of 10m from the ground. How long does it take for the projectile to hit the ground?
Calculate the flight time of a ball moving in parabolic motion, with initial velocity 5.0m/s at angle 30 degrees from the horizontal travelling for 23 metres.
Suggest which particles will be emitted as K-40 decays to Ca-39:
Describe the interaction that is responsible for keeping protons and neutrons together in a stable nucleus.