Question

The planet Venus has a mass of 4.87 × 10^24 kg, and Earth has a mass of 5.97 × 10^24 kg. How far apart are the two planets when they exert a gravitational force of 1.12 × 10^18 N on one another?

Answer 1

Taking into account the Universal Law of Gravitation, Venus and Earth are separated by a distance of 1,316,302,384 m.

Universal Law of Gravitation

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:

$F=G\frac{Mm}{d^{2} }$

where:

• G is the universal gravitational constant, with a value of 6.67×10⁻¹¹ $\frac{Nm^{2} }{kg^{2} }$.
• M and m are the masses of the bodies that interact.
• d is the distance that separates them.

Distance of Venos and Earth

In this case, you know:

• F= 1.12×10¹⁸ N
• G= 6.67×10⁻¹¹ $\frac{Nm^{2} }{kg^{2} }$
• M= mass of Venus= 4.87×10²⁴ kg
• m= mass of Earth= 5.97×10²⁴ kg
• d= ?

Replacing in the Universal Law of Gravitation:

$1.12x10^{18} N=6.67x10^{-11} \frac{Nm^{2} }{kg^{2} }\frac{4.87x10^{24} kgx5.97x10^{24} kg}{d^{2} }$

Solving:

$1.12x10^{18} N=6.67x10^{-11} \frac{Nm^{2} }{kg^{2} }\frac{2.90739x10^{49} kg^{2} }{d^{2} }$

1.12×10¹⁸ N÷ 6.67×10⁻¹¹ $\frac{Nm^{2} }{kg^{2} }$= $\frac{2.90739x10^{49} kg^{2} }{d^{2} }$

1.678×10 ²⁸$\frac{kg^{2} }{m^{2} }$= $\frac{2.90739x10^{49} kg^{2} }{d^{2} }$

1.678×10 ²⁸$\frac{kg^{2} }{m^{2} }$× d²= 2.90739× 10⁴⁹ kg²

d²= 2.90739× 10⁴⁹ kg²÷ 1.678×10 ²⁸$\frac{kg^{2} }{m^{2} }$

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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