Mass

Mass is a property of objects that determines how strongly it resists acceleration and the strength of its gravitational field. These two definitions of mass are identical, a property known as the equivalence principle.

It has units of [mass].

Classical Mechanics

Mass shows up in classical mechanics in two places: in Newton's law, and in the gravitational potential from a point mass.

Newton's law relates force F and acceleration a as on a point mass of mass m as $\vec{F} = m \vec{a}$. Given the forces acting on a point mass, the acceleration can be determined, or vice versa. One definition of mass follows from Lagrangian mechanics: the kinetic energy term in the Lagrangian can be defined to be $T = \frac{1}{2} m \dot{x}^2$.

Newton's law of gravitation states that the gravitational potential on a point mass with position vector r' due to a point mass of mass M with position vector r is $V = \frac{GM}{\left| \vec{r} - \vec{r}' \right|}$. The gravitational potential energy U of the point mass is its mass multiplied by V.

The gravitational field is the negative of the gradient of gravitational potential, given by $\vec{g} = - \nabla V = \frac{GM}{\left( \vec{r} - \vec{r}' \right)^2}$. The gravitational force F on the point mass is the negative of gradient of the gravitational potential energy, or its mass multiplied by g.

Masses

The following are the masses of some physical objects

Mass	Object
9.11×10-31 kg	Electron
4.10×10-30 kg	Up Quark
8.56×10-30 kg	Down Quark
1.69×10-28 kg	Strange Quark
1.90×10-28 kg	Muon
1.67×10-27 kg	Proton
1.68×10-27 kg	Neutron
2.30×10-27 kg	Charm Quark
7.45×10-27 kg	Bottom Quark
3.07×10-25 kg	Top Quark
2.20×10-8 kg	Planck mass
1.00×1013 kg	67P/Churyumov–Gerasimenko
2.67×1019 kg	3 Juno
5.97×1024 kg	Earth ~Type 1.0 Civilization
1.99×1030 kg	the Sun ~Type 2.0 Civilization
9.50×1041 kg	the Milky Way ~Type 3.0 Civilization
3.04×1054 kg	the Observable Universe ~Type 4.0 Civilization