the sky shortly after sunset. Joe spots a very bright object rising in the east and both he and Tom know it must be a planet. Joe claims it must be Venus but Tom insists that it's Jupiter. Who must be wrong?
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Short answer is Venus is never seen on the far side of the Sky from the Sun, so it must be Jupiter.
It cannot be Venus because Venus orbits closer to the Sun than Earth, so Earth can never pass between Venus and the Sun. When looking to the east at a planet at the time of sunset, the setting Sun in the west is behind you. So you must be standing between that planet and the Sun, and since you are standing on Earth, Earth must be between that planet and the Sun, so that planet cannot be closer to the Sun than Earth, so it cannot be Venus.
It cannot be Venus because Venus orbits closer to the Sun than Earth, so Earth can never pass between Venus and the Sun. When looking to the east at a planet at the time of sunset, the setting Sun in the west is behind you. So you must be standing between that planet and the Sun, and since you are standing on Earth, Earth must be between that planet and the Sun, so that planet cannot be closer to the Sun than Earth, so it cannot be Venus.