represent a gravitational field by means of field lines

What is a Gravitational Field?

A gravitational field is a region around a mass where another mass feels a force.

The field is described by the vector field \$\mathbf{g}\$:

\$\mathbf{g} = -\,G\,\frac{M}{r^{2}}\;\hat{\mathbf{r}}\$

where \$G\$ is the gravitational constant, \$M\$ the source mass, \$r\$ the distance, and \$\hat{\mathbf{r}}\$ the radial unit vector pointing away from the source.

Think of the field like invisible “gravity waves” that spread out from every mass.

Field Lines: A Visual Tool

• Direction: Field lines point toward the mass for gravity (opposite to electric field lines).
• Density: The closer the lines, the stronger the field.
• Never Cross: Two field lines can never intersect.
• Start/End: For gravity, lines start at infinity and end on the mass.

🔍 Analogy: Imagine a crowd of people walking toward a stadium. The crowd density is higher near the stadium entrance – that’s like field line density.

Step‑by‑Step Guide

1. Choose a point outside the mass.
2. Draw a short line segment pointing toward the mass.
3. At the end of that segment, draw another short segment still pointing toward the mass.
4. Continue until the line reaches the mass.
5. Repeat from several starting points to show the field’s shape.

💡 Tip: Use a ruler or a straightedge to keep lines straight and evenly spaced.

Single Mass (e.g., Earth)

For a single spherical mass, field lines are radial and evenly spaced.

The field strength at a distance \$r\$ is:

\$|\mathbf{g}| = G\,\frac{M}{r^{2}}\$

🪐 Visual: Imagine a set of concentric circles around Earth, each circle representing a constant field strength.

Two Equal Masses (Binary System)

Field lines start at infinity, bend toward each mass, and converge at the centre of mass.

Between the masses, lines are denser, showing a stronger combined field.

⚖️ Analogy: Two magnets pulling a metal ball toward the middle.

What to Include in Your Answers

• State the direction of field lines (toward the mass).
• Show that lines are denser where the field is stronger.
• Explain why lines never cross.
• Use correct LaTeX notation for equations.

Drawing Practice

1. Start with a single mass; draw at least 4 field lines.
2. Move to a two‑mass system; show the convergence point.
3. Label the direction and field strength qualitatively.

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Remember: Clear, neat drawings with consistent spacing score higher.