More Information.

Newton's Law of Universal Gravitation


\( F = G {m_1 . m_2 \over d^2} \)
Where

F = the force of gravity between two objects.
G = the universal gravitational constant.
m1 = the mass of object 1.
m2 = the mass of object 2.
d = the the distance between the two objects' centres of gravity.

Examples


Example 1 - Acceleration due to gravity.


For this example I'm going to be using Newton's second law \(F = ma \) where F = force, m = mass and a = acceleration. I'm going to use 6.6743 × 10-11 m3 kg-1 s-2 for the universal gravitational constant

I will call the universal gravitation formula equation 1 and the second law formula equation 2.

Consider an object with a mass m1 on a planet or satellite with a mass m2. The distance between the centres of gravity of m1 and m2 is d. Combining equations 1 and 2 we get:

\( a = {G m_2 \over d^2} \)


So for planet Earth and our nearest neighbours, using the above equation and a mobile phone calculator, I get the following:

Object Mass (kg) Distance from Surface
To Centre of Mass d2 (m) 		Acceleration due
to Gravity (m/s2)
Earth 5.972 × 1024 6371000 9.820
The Moon 7.348 × 1022 1737500 1.624
Venus 4.867 × 1024 6052000 8.869
Mars 6.391 × 1023 3389500 3.712

Example 2 - Calculate the mass of a planet.


First I need to introduce a new equation, the equation for centripetal force. We can call this Equation 3.

\( F_c = {m_1v^2 \over d} \)


Where Fc is the net force pushing the object with a mass m1 away from the centre of gravity of the object with a mass m2 due to it's velocity v.

Combining equations 1 and 3 for a stable orbit we get:

\(G {m_2 \over d^2} = {v^2 \over d} \)
because for a stable orbit F and Fc must be equal and the m1 on both sides of the equation cancel out. Rearranging this equation we get:

\(m_2 = {d v^2 \over {G}}\)



Sir Isaac Newtons



This page is a sort of Sir Isaac Newton tribute. Because of the way my education went, Newton is one of the few great scientists whose work I can understand. Anyone who knows me well knows my great admiration for this genius.

Here's his laws of motion:

1. The Law of Inertia


An object at rest stays at rest, and an object in motion remains in motion at a constant speed in a straight line, unless acted upon by an external unbalanced force.

2. The Law of Force


The acceleration of an object depends directly on the net force acting on it and inversely on its mass.

3. The Law of Action and Reaction


For every action, there is an equal and opposite reaction. When two objects interact, they apply forces to each other of equal magnitude and opposite