The maximum and minimum distances of a planet from the centre of the sun are 2R and 4R respectively, where R is radius of sun. Let M be the mass of sun.then the maximum speed of planet is

from conservation of angular momentum       mvr=constant mv12R=mv24R            v1=2v2 from conservation of energy12mv12-GMm2R=12mv22-GMm4R  =12 mv122-GMm4R 12mv12 -12 mv122 =GMm2R-GMm4R 38mv12 =GMm4R v1=2GM3R