## Conventional gravitational massEdit

Kepler $ \mu = 4 \pi^2 \frac{Distance^3}{Time^2} \propto Gravitational \, Mass $

Galileo found that for an object in free fall, the distance that the object has fallen is always proportional to the square of the elapsed time:

- $ g = \frac{Distance}{Time^2} \propto Gravitational \, Field $

### Newtonian Gravitational mass Edit

The Newtonian concept of gravitational mass rests on Newton's law of gravitation. Let us suppose we have two objects A and B, separated by a distance *r*_{AB}. The law of gravitation states that if A and B have gravitational masses *M*_{A} and *M*_{B} respectively, then each object exerts a gravitational force on the other, of magnitude

- $ F = G \, \frac{M_{\mathrm{A}} M_{\mathrm{B}}}{(r_{\mathrm{AB}})^2} \, , $

where *G* is the universal gravitational constant. The above statement may be reformulated in the following way: if *g* is the acceleration of a reference mass at a given location in a gravitational field, then the gravitational force on an object with gravitational mass *M* is

- $ F = Mg \, . $

This is the basis by which masses are determined by weighing. In simple spring scales, for example, the force *F* is proportional to the displacement of the spring beneath the weighing pan, as per Hooke's law, and the scales are calibrated to take *g* into account, allowing the mass *M* to be read off. A balance measures gravitational mass; only the spring scale measures weight.

## Photo-gravitational mass of central bodyEdit

To find the total absolute Momentum of light radiated for an object from mass m, we have to take into account the surface area, A(in m^{2}) of the astronomic object:

- $ P = k A j^{\star} = k A \varepsilon\sigma T_s^{4}. $

where *j* is known variously as the black-body **irradiance**, **energy flux density**, **radiant flux**, or the **emissive power**
and k is proportional constant.
The constant of proportionality σ, called the Stefan–Boltzmann constant or **Stefan's constant**, is non-fundamental in the sense that it derives from other known constants of nature. The value of the constant is

- $ \sigma=\frac{2\pi^5 k^4}{15c^2h^3}= 5.670 400 \times 10^{-8} \textrm{J\,s}^{-1}\textrm{m}^{-2}\textrm{K}^{-4} $

where k is the Boltzmann constant, h is Planck's constant, and c is the speed of light in a vacuum. Thus at 100 K the energy flux density is 5.67 W/m^{2}, at 1000 K 56,700 W/m^{2}, etc.

Define Photogavitational mass as follows,

$ m_{pg} = k_{pg} T_s^4 $

Where $ m_i $ is inertial mass and $ k_{pg} $ is photogravitational constant. However without bulk, the surface temperature couldn't be maintained. With T cube inertial mass assumption,

$ T^4 = k_x m_i T_s $

and can be written as follows.

$ m_{pg} = m_i T_s /T_0 $

Thus Momentum from unit area $ P/A =k_p M_i T_s $

The difference between surface temperature and core temperature is also important for near field gravity. with lattitude, it increases resulting in value between 9.78 and 9.82 m/s2

## Physical quantityEdit

It is important to check physical meaning of $ M_i T_s /T_0 $. The value is proportional to the pressure for ideal gas.

The Physical quantity is proportional to the radiational pressure for solid.

## See alsoEdit

- Stefan–Boltzmann law
- AME
- Mass
- Esther -electra
- Photogravity