Question

You are a mad scientist who wants to create a parallel universe with a gravitationnal constant G-0. In order to have planetary motion, you give a positive charge to the central star and a negative charge to the planets. If the sun has a charge of 7,580 exaCoulombs (10 18 C), what should be the charge of earth (absolute value) so that it still has a period of 365 days? Give your answer in teraCoulombs (1012 C). Use the following constants: 2 єд 8.854x10-12 C2 /N nm MSun 1.988 x 1030 kg MEarth 5.962 x 1024 kg DSun-Earth 1.496 x 10 m Note : The value for the charge of the sun is different for all students. There might be a comma in the number; it is NOT a decimal separator but rather an old fashioned thousand separator. Simply ignore it the value for the charge has no decimals. Note 2: Of course you can assume that you are able to create a mysterious force that will allow the stars and planet to stick together despite zero gravity! Your Answer

Answer 1

For this kind of universe, the centrifugal force on Earth must be counter balanced by the Coulombic attraction force.

If Earth still has a period of 365 days then the angular velocity of the Earth can be calculated as

So, the centrifugal force will be

Where, m = 5.962 x 10²⁴ is mass of Earth

R = 1.496 x 10¹¹ m is distance between Earth and Sun

So,

Let the charge on Earth is -Q coulomb.

Given, charge on Sun (q) = 7580 x 10¹⁸ C

distance between Earth and Sun (R) = 1.496 x 10¹¹ m

So, the electrostatic force between them will be

Where,

  

So,

  

For a stable system ,

or,   

or,   

Hence, 11.6 tera coulombs of negative charge is placed on the Earth.

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