How many stronger is the gravitational force between Venus (`R_(Ven us)` =0.723 AU, `M_(Ven us)` =0.815 `M_(Earth)`) and the Sun when compared to the gravitational force between Earth and the Sun. `F=G*(m_1*m_2)/r^2.`

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

`G*(m_1*m_2)/r^2,`

where `G` is the gravitational constant, `m_1` and `m_2` are the masses of the bodies and `r` is the distance between them. The value of G isn't necessary for this problem.

For Venus and the Sun the force is  `G*(M_(Ven us)*M_(Sun))/(R_(Ven us))^2,`

for Earth and the Sun the force is  `G*(M_(Earth)*M_(Sun))/(R_(Earth))^2.`

So, the ratio between them is  `(M_(Ven us)/M_(Earth))*(R_(Earth)/R_(Ven us))^2.` 

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

So the ratio is  `0.815*(1/0.723)^2 approx 1.56` (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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