Question

Earth takes 365 days to orbit Sun, while Venus takes 225 days. If Earth and Venus are in perfect alignment with Sun on a day, in how many days will this happen again?

Answer 1

Answer:

How often do alignments happen? Earth takes 365 days to travel one complete orbit, while Mercury takes 88 days and Venus takes 224 days, so the time between alignments will require each planet to make a whole number of orbits around the Sun and return to the pattern you see in the figure.

Answer 2

This condition of perfect alignment will happen again in 16,425 days.

Given:

Days taken by earth to orbit sun = 365

Days taken by Venus to orbit sun = 225

To find: When they will be perfectly aligned again

Solution:

We know that the earth and venus began at the same position

⇒ number of days taken to reach the same position together again = Least Common Multiple of 365 and 225

⇒ Number of days = LCM (365, 225)

⇒ Number of days = 16,425

∴ They will be perfectly aligned again in 16,425 days Answer

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