Physics 316, Problem Set 4, due Tuesday October 25 in class 1. Earth-Venus highway In the year 2145, in response to an economic recession, the government launches a project to build a bridge between Earth and Venus. The bridge will be made of modern materials so that its mass will be negligible compared to that of either planet. It will make a rigid connection between Earth and Venus so that their distance will be ﬁxed at their current distance 2 L of closest approach. However, doom-sayer scientists decry the project, saying that it will perturb the orbit of the earth. Assess this claim, taking the Earth’s radius to be R , and both masses to be m . Consider both orbits to be circular before the planets are joined. Treat both planets as point masses and neglect any eﬀects due to rotation of the planets about their axis. (The bridge is to be installed so that it doesn’t interfere with this rotation). Take as co-ordinates the radial distance r from the sun to the center of the bridge, and its orbital angle
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