Newton’s Law of Universal Gravitation

Yaser Rahmati | یاسر رحمتی

Definition

According to Newton’s law of universal gravitation, a body of mass $m_{1}$ attracts another body of mass $m_{2}$ with an amount of force $F$ according to the formula:

$$F=G\frac{m_{1}m_{2}}{r^{2}}$$

where $r$ is the distance between the two bodies and $G$ is the gravitational constant.

Example

Let’s take the masses of two bodies:

• The mass of the first body ($m_{1}$) is 0.5 kg,

• The mass of the second body ($m_{2}$) is 1.5 kg.

• The value of the gravitational constant is $6.674\times10^{-11} N.m^2.kg^{-2}$ .

• ow we’re ready to calculate the gravitational force in the ow we’re ready to calculate the gravitational force between between 10m to 500 m.

import sympy as sp

# Define the symbolic variable
r = sp.symbols('r')

# Constant, G
G = 6.674*(10**-11)

# Two masses
m1 = 0.5
m2 = 1.5

# Define the function symbolically
F=G*m1*m2/(r**2)

sp.plot(F , (r, 10, 500), axis_center= (0,0))

We want to see what happens to the force as the distance between the two bodies increases.

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