Gravity and mass
Sir Isaac Newton is often visualised with an apple falling from a tree.
The real meaning of Newton's work on gravitation concerns the attractive A push or a pull. The unit of force is the newton (N). which exists between any two masses simply because they have The amount of matter an object contains. Mass is measured in kilograms (kg) or grams (g)..
Every point mass attracts every single other point mass by a force pointing along the line intersecting both points.
The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them.
Newton's Law of Universal Gravitation is written as:
\(F=G\frac{m_1m_2}{r^2}\)
The constant of proportionality is the universal gravitational constant ("big G") which equals \(6.674\times{10^{- 11}}N{m^2}k{g^{- 2}}\).
Overall this equation is simpler than it looks as long as you ensure that:
- distance is given between centres
- units are all in metres and kilograms
The force of gravity exists between all objects. The closer together the objects are, the more noticeable the effect. But gravity only becomes noticeable when you have at least one very big mass (a planet for example).
Question
A planet is a third of the distance from a star as another planet of the same mass. Will it have three times the gravitational attraction?
No, the distance is squared in the equation so it would have nine times the force (a third of the distance squared gives a nine-fold increase in force)
\(F = \frac{{G{m_1}{m_2}}}{{{r^2}}}\)
\(F=\frac{{G{m1}{m2}}}{{{(\frac{1}{3}\times r)^2}}}\)
\(F=\frac{{G{m1}{m2}}}{{{\frac{1}{9}\times r^2}}}\)
\(F=\frac{{9G{m1}{m2}}}{{{r^2}}}\)