Saturday, March 22, 2014

How many stronger is the gravitational force between Venus ( =0.723 AU, =0.815 ) and the Sun when compared to...

Hello!


You are right. By Newton's Law of universal gravitation the gravitational force between two bodies is:



where is the gravitational constant, and are the masses of the bodies and is the distance between them. The value of G isn't necessary for this problem.


For Venus and the Sun the force is  


for Earth and the Sun the force is  


So, the ratio between them is   


Note that the mass of Venus is given in terms of Earth's mass and that one A.U. is actually (by definition).


So the ratio is   (times). This is the answer.


Despite this, the gravity on Venus is slightly less then on Earth. Of course this depends on Venus' radius and Earth's radius, not on their distances from the Sun.

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