TidalScience

• Force Due to Gravity
• Tidal Forces

Double Bulge

• Spring/Neap Tides

Force Due to Gravity

The force due to gravity between two objects <math>m_1</math> and <math>m_2</math> is defined by the following equation.

<math> F_{12} = \frac{-Gm_1m_2}{r^2} </math>

<math> \begin{align} F_{12} &=& \mbox{gravitational force between }m_1\mbox{ and }m_2 \\ m_1 &=& \mbox{mass of object 1} \\ m_2 &=& \mbox{mass of object 2} \\ G &=& \mbox{gravitational constant }(6.673*10^{-11}m^3kg^{-1}s^{-2}) \\ r &=& \mbox{distance between the centers of }m_1\mbox{ and }m_2 \\ \end{align} </math>

Tidal Forces

The tidal force is the rate of change of gravity with distance. For the math minded you can differentiate the equation of force due to gravity, or approximate the tidal force by finding the gravitational force differences between two points.

<math> F_{cg} = \frac{-Gm_1}{r^2} </math>

<math> \begin{align} F_{cg} &=& \mbox{gravitational force between }m_1\mbox{ to the center of the Earth } \\ m_1 &=& \mbox{mass of object 1} \\ G &=& \mbox{gravitational constant }(6.673*10^{-11}m^{3}kg^{-1}s^{-2}) \\ r &=& \mbox{distance between the centers of }m_1\mbox{ and }m_2 \\ \end{align} </math>

<math> F_{ng} = \frac{-Gm_1}{\left (r - R_{earth}\right) ^2} </math>

<math> \begin{align} F_{ng} &=& \mbox{gravitational force from }m_1\mbox{ to the nearest surface of the Earth to }m_1 \\ m_1 &=& \mbox{mass of object 1} \\ G &=& \mbox{gravitational constant }(6.673*10^{-11}m^{3}kg^{-1}s^{-2}) \\ r &=& \mbox{distance between the centers of }m_1\mbox{ and }m_2 \\ R_{earth} &=& \mbox{radius of the Earth} \\ \end{align} </math>

<math> F_{fg} = \frac{-Gm_1}{\left (r + R_{earth}\right) ^2} </math>

<math> \begin{align} F_{fg} &=& \mbox{gravitational force from }m_1\mbox{ to the farthest surface of the Earth from }m_1 \\ m_1 &=& \mbox{mass of object 1} \\ G &=& \mbox{gravitational constant }(6.673*10^{-11}m^{3}kg^{-1}s^{-2}) \\ r &=& \mbox{distance between the centers of }m_1\mbox{ and }m_2 \\ R_{earth} &=& \mbox{radius of the Earth} \\ \end{align} </math>

Double Bulge

Spring/Neap Tides