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Gravitational Field

Field of force due to point mass

Library

Forces and Torques

Description

This block represents the gravitational field of a point mass. Rigid bodies in this field experience a gravitational force as a function of mass and distance. The field strength, and therefore the force magnitude, decays with increasing distance from the point mass source according to Newton's law of universal gravitation:

where:

  • Fg is the gravitational force that the source point mass exerts on a target rigid body.

  • G is the universal gravitational constant, 6.67384 × 10-11 m3kg-1s-2.

  • M is the source point mass that you specify.

  • m is the total mass of the target rigid body that the gravitational field acts upon.

  • RBF is the distance between the source mass and the target rigid body that the gravitational field acts upon.

The figure shows these variables. The plot shows the inverse square dependence between the gravitational force and distance.

The source mass can take on positive and negative values. Combine multiple instances of this block to model the gravitational effects that positive and negative mass disturbances impose on a stronger gravitational field, such as a reduction in the gravitational pull of a planet due to a concentration of low-density material along a portion of its surface.

Whether the gravitational force is attractive or repulsive depends on the signs of the source and target masses. The table summarizes the conditions under which the gravitational force is attractive, i.e., negative in magnitude, or repulsive, i.e., positive in magnitude.

This block excludes the gravitational forces that other rigid bodies exert on the field source mass. To include these forces, you can connect Gravitational Field blocks to other rigid bodies in the model. Alternatively, you can use the Inverse Square Law Force block to model the gravitational forces between a single pair of rigid bodies.

The gravitational field is time invariant. To specify a time-varying, spatially uniform field, use the Mechanism Configuration block.

Dialog Box and Parameters

Mass

Aggregate mass responsible for the gravitational field. This mass exerts a gravitational force on each rigid body present in the same mechanism according to Newton's law of universal gravitation.

Inertial effects are ignored, i.e., the mass provides zero resistance to acceleration. To include inertial effects, connect this block to one or more Solid or Inertia blocks.

The default value for the mass parameter is 1.0 kg.

Ports

Frame port F represents a frame with origin at the point mass responsible for the gravitational field.

See Also

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