Gravity is a universal force. It is one of the four fundamental forces that act on us all the time. The strong force and the weak force act only inside the centre of atoms. The electromagnetic force rules objects with excess charge such as electrons and protons. Gravity affects objects with mass.
Sir Isaac Newton published in his treatise ‘Philosophiae Naturalis Principia Mathematica’ in 1687 his universal law of gravitation.
If a stone is thrown up it will come down, unless it is thrown up at a velocity that is so fast, if we neglect the effects of friction, it allows the stone to leave the Earth and never return. This is called the escape velocity of the Earth. The energy of an object in motion is called kinetic energy:
Kinetic energy = ½mv²
where m is the mass of the object in kg, v is its velocity in metres/sec and energy is in Joules.
A body in the Earth’s gravitational field on the Earth’s surface has stored energy called gravitational potential energy:
Gravitational potential energy = -ᴳᴹᵐ⁄ᵣ
Where G is the universal gravitational constant, M is the mass of the larger object (Earth), m is the mass of the smaller object and r is the distance between them (radius of the Earth). The minus sign means that energy has to be given to the smaller object to increase its distance from the centre of the larger object (the centre of the Earth). Ignoring the minus sign, to leave the Earth’s gravitational field the object must be given enough kinetic energy to overcome its gravitational potential energy:
½mv² = ᴳᴹᵐ⁄ᵣ
therefore ½v² = ᴳᴹ⁄ᵣ
So v² = ²ᴳᴹ⁄ᵣ
v = √(²ᴳᴹ⁄ᵣ)
From this, one can see that the escape velocity of a planet is solely dependent on its mass and its radius.
The average velocity of molecules of gas is around 0.5m/s with smaller molecules travelling faster than larger ones. So hydrogen and helium have faster velocities and the Earth has lost most of these gases due to their molecules travelling faster than escape velocity.
Acceleration due to gravity
It is alleged that Galileo dropped a large and a small metal sphere from the leaning tower of Pisa at the same time and they both hit the ground at the same time. This showed that, neglecting the effect of air resistance, bodies undergo the same rate of acceleration when they are near the surface of the Earth, irrespective of their mass. This acceleration is called the acceleration due to gravity (g) and it has a value of 9.81 m/s² near the surface of the Earth.
Newton’s second law of motion states that for objects with a constant mass and acceleration:
Force = mass x acceleration (F = ma),
So F = ma becomes F = mg
Using the universal law of gravitation:
F=ᴳᴹᵐ⁄ᵣ²
therefore, mg = ᴳᴹᵐ⁄ᵣ²
So g = ᴳᴹ⁄ᵣ₂
We know escape velocity v = √(²ᴳᴹ⁄ᵣ) so if we put this in terms of the acceleration due to gravity:
v = √2gr
When an object is at rest it will exert a force F (F = mg) on whatever supports it and we know this as the weight of the object.
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