Skip to content
\( F \) is the gravitational force in Newtons (N).\( m \) is the mass of the object in kilograms (kg).\( g \) is the acceleration due to gravity in meters per second squared (m/s²).
\( F \) is the gravitational force between two masses.\( G \) is the gravitational constant, approximately \( 6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \).\( m_1 \) and \( m_2 \) are the masses of the two objects.\( r \) is the distance between the centers of the two masses.
Gravitational Fields
Lesson on Gravitational Fields
Uniform Gravitational Fields
In a uniform gravitational field, the gravitational force is constant in both magnitude and direction. This occurs near the surface of the Earth where the gravitational field strength \( g \) is approximately \( 9.81 \, \text{m/s}^2 \).
Mathematical Representation
The gravitational force 
acting on an object of mass, m, in a uniform field is given by:
Where:
Example Calculation
If a mass \( m = 10 \, \text{kg} \) is placed in a uniform gravitational field, the force acting on it can be calculated as follows:
\[
F = 10 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 = 98.1 \, \text{N}
\]
Non-Uniform Gravitational Fields
In contrast to uniform fields, non-uniform gravitational fields have variations in gravitational force depending on the position within the field. This can occur in scenarios where the distance from the mass generating the field changes significantly, such as when moving away from the Earth or near massive celestial bodies.
Mathematical Representation
The gravitational force in a non-uniform field can be described by Newton's law of universal gravitation:
\[
F = \frac{G \cdot m_1 \cdot m_2}{r^2}
\]
Where:
Example Calculation
If we consider two objects, a mass \( m_1 = 5 \, \text{kg} \) and a mass \( m_2 = 10 \, \text{kg} \) separated by a distance \( r = 2 \, \text{m} \), the gravitational force can be calculated as follows:
\[
F = \frac{6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \cdot 5 \, \text{kg} \cdot 10 \, \text{kg}}{(2 \, \text{m})^2}
\]
Calculating this gives:
\[
F = \frac{6.674 \times 10^{-11} \cdot 50}{4} = \frac{3.337 \times 10^{-9}}{4} = 8.3425 \times 10^{-10} \, \text{N}
\]
### Conclusion
Want to print your doc?
This is not the way.
This is not the way.
Try clicking the ··· in the right corner or using a keyboard shortcut (
CtrlP
) instead.