Gravitational Fields I

Introduction

The attraction of bodies because of their mass can be described by gravitational fields. The figures show the so-called field lines, which run along the force of gravity.

Radial gravitational field of the earth

The gravitational field of the earth is a radial field, that is the gravitational force always acts toward the center of the Earth and its magnitude is inversely proportional to the distance.


Distance to ground (surface of the Earth)
\( h \) = a \( \rm km \)

Distance to center of the Earth
\( r \) = a \( \rm km \)

Gravitational force
\( F \) = a \( \rm N \)

\( F = G \cdot \dfrac{m_1 \cdot m_2}{r^2} \)

(The sample mass (green) can be moved with the mouse. The gravitational force (red) is then calculated from the distance to the ground.)

Gravitational field near to the ground surface

Near the Earth's surface the gravitational field can be considered to be homogeneous, that is the gravitational force is always directed to the earth's surface and the gravitational acceleration is constant: \( g = \rm 9,81 \,\, \frac{m}{s^2} \).

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Distance to ground (surface of the Earth)
\( h \) = ? \( \rm m \)

Distance to center of the Earth
\( r \) = ? \( \rm m \)

Gravitational force
\( F \) = ? \( \rm N \)

\( F = m \cdot g \)


(The sample mass (green) can be moved with the mouse. The gravitational force (red) is then calculated from the distance to the ground.)

Gravitational acceleration

The gravitational acceleration is the magnitude of a gravitational field regardless of mass of a sample. The formulas were derived using \( a = \frac{F}{m} \) from the gravitational force.


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