It takes the earth 1 yr to travel around the sun It takes Venus 615 years to orbit the sun If the planets are in a straight line with the sun now how long will it be before this is the case again?

Answer 1

It certainly doesn't take Venus 615 years to orbit the Sun. Venus is closer to the Sun than Earth, therefore, it will take Venus LESS time to orbit the Sun than Earth, that is, less than a year. If you look it up in the Wikipedia, it is about 0.615 years.

You can also look up the "synodic period" (every how often Venus catches up with Earth), which is 584 days. This is calculated as follows: In a year, Earth does one revolution around the Sun. In the same year, Venus does 1 / 0.615 revolutions around the Sun, that is, about 1.63 revolutions. Therefore, every year Venus does 0.63 revolutions more than Earth. For Venus to catch up, it will have to do a full revolution more than Earth; the time it takes to do this is 1 / 0.63 = 1.59 years. You may want to repeat the calculation with more significant digits, but that is the general idea.