# Formula: Stable Circular Orbit at the Surface of a Celestial Body Velocity    Radius    Mass    Gravitational constant

## Velocity

Unit
Tangential velocity of the body (e.g. satellite) on the orbit around a planet, a star or another central body near its surface. Only with this velocity the body remains without propulsion on its circular orbit around the central body without falling on the central body or moving further away from it.

In order for the body to orbit the earth at the earth's surface without propulsion, the following velocity of the body is required: $\class{blue}{v_1} ~=~ \sqrt{ \frac{6.67 \cdot 10^{-11} \frac{\mathrm N \, \mathrm{m}^2}{\mathrm{kg}^2} ~\cdot~5.97 \cdot 10^{24}\,\mathrm{kg} }{6.38 \cdot 10^6 \,\mathrm{m}} } ~=~ 7.9 \, \frac{\mathrm{km}}{\mathrm s}$

Unit
Radius of the celestial body. For example the radius of the earth.

## Mass

Unit
Mass of the central body around which a satellite should orbit. In the case of the earth the mass is: $$\class{brown}{M} ~=~ 5.972 \cdot 10^{24} \, \mathrm{kg}$$.

The larger the mass of the central body, the larger the orbital velocity $$\class{blue}{v_1}$$ of the satellite must be to orbit the central body without propulsion.

## Gravitational constant

Unit
The gravitational constant is a physical constant that occurs in equations describing the interaction between masses. It has the following experimentally determined value: $$G ~\approx~ 6.674 \, 30 ~\cdot~ 10^{-11} \, \frac{ \mathrm{m}^3 }{ \mathrm{kg} \, \mathrm{s}^2 }$$

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