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Taking into account the Universal Law of Gravitation, Venus and Earth are separated by a distance of 1,316,302,384 m.
The Universal Law of Gravitation establishes that bodies, by the simple fact of having mass, experience a force of attraction towards other bodies with mass, called gravitational force.
The Universal Law of Gravitation states that the gravitational force between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance that separates them. Mathematically it is expressed as follows:
[tex]F=G\frac{Mm}{d^{2} }[/tex]
where:
In this case, you know:
Replacing in the Universal Law of Gravitation:
[tex]1.12x10^{18} N=6.67x10^{-11} \frac{Nm^{2} }{kg^{2} }\frac{4.87x10^{24} kgx5.97x10^{24} kg}{d^{2} }[/tex]
Solving:
[tex]1.12x10^{18} N=6.67x10^{-11} \frac{Nm^{2} }{kg^{2} }\frac{2.90739x10^{49} kg^{2} }{d^{2} }[/tex]
1.12×10¹⁸ N÷ 6.67×10⁻¹¹ [tex]\frac{Nm^{2} }{kg^{2} }[/tex]= [tex]\frac{2.90739x10^{49} kg^{2} }{d^{2} }[/tex]
1.678×10 ²⁸[tex]\frac{kg^{2} }{m^{2} }[/tex]= [tex]\frac{2.90739x10^{49} kg^{2} }{d^{2} }[/tex]
1.678×10 ²⁸[tex]\frac{kg^{2} }{m^{2} }[/tex]× d²= 2.90739× 10⁴⁹ kg²
d²= 2.90739× 10⁴⁹ kg²÷ 1.678×10 ²⁸[tex]\frac{kg^{2} }{m^{2} }[/tex]
d²= 1.73265 m²
d= √1.73265 m²
d=1,316,302,384 m
Finally, Venus and Earth are separated by a distance of 1,316,302,384 m.
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