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Riddles

 Refer to the hints section below if you need them.


  1. On Dec 21, 2020, Saturn and Jupiter appeared in the sky to have a conjunction. They were in the same sign/rashi. Saturn takes 30 years to go around the Sun, while Jupiter takes 12 years. After how many years will they appear to be in the same sign again (not necessarily as close to have the conjunction we witnessed last December)? There are 2 possible answers although only one of them is possible in reality. What are the answers?


  1. On a fine day in June, I travel 10 kms North and then I travel 5 kms South. How far am I from my original location? I am not looking for the obvious answer of 5 kms North? What are the other answers?


  1. When a person is watching the lunar eclipse, his friend calls him and says that he is watching the Solar eclipse. How is this possible? Both of them are telling the truth.


  1. Consider an object which is falling to the Earth from great heights. As it approaches the Earth, it experiences increasing gravity. Now imagine that the object falls into a hole after reaching the surface of the Earth. The hole is deep enough to reach the center of the Earth. Will the object continue to experience increasing gravity or a steady gravity or decreasing gravity? Explain your answer as to why.


  1. Derive a formula to calculate the length of the arc of Earth’s surface that a plane flying at a height of h will see.


  1. Calculate the daylight hours for a given latitude on solstice. Extra credit - extend the formula to calculate on any day of the year (you can use days from solstice or equinox).

Hints


  1. Use angular speed and velocities to arrive at both the answers.

  2. You can change the directions (go South first and then go North), but then you may want to change the month to December

  3. This type of conversation was not possible before 1969

 Their third friend says that he is watching both the Solar and lunar    eclipses.

  1. What will be the gravity at the center of the Earth?

  2. Use basic trigonometry

  3. Use basic trigonometry and make reasonable assumptions

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