1. What is a Gravitational Field?
A gravitational field is a region around a mass where another mass experiences a force of attraction. Every object with mass creates a gravitational field around itself—even you—but only very large masses like Earth produce noticeable effects.
Instead of thinking of gravity as two objects pulling each other, it is helpful to imagine that a mass sets up a field, and any other mass placed in that field feels a force.
1.1. Field Lines
Gravitational field lines help visualize how gravity acts:
- They point towards the mass (gravity is always attractive).
- The closer the lines, the stronger the field.
- They never intersect.
1.1.1. Examples
- Earth’s field pulls objects toward its centre.
- The Sun’s gravitational field holds planets in orbit.
2. Gravitational Field Strength
The gravitational field strength at a point is defined as the force experienced by a unit mass placed at that point.
\( g = \dfrac{F}{m} \)
For Earth, near the surface, \( g \approx 9.8\,\text{m/s}^2 \).
2.1. Field Strength at Distance r from Earth
\( g = \dfrac{GM}{r^2} \)
This shows that the field becomes weaker as we move farther from Earth.
3. What is Gravitational Potential?
Gravitational potential at a point is the work done per unit mass to bring a small object from infinity to that point, against gravity.
It is a measure of how much energy a mass would have due to its position in a gravitational field.
Gravitational potential is a scalar quantity.
3.1. Formula for Gravitational Potential
The gravitational potential at distance \( r \) from a mass is:
\( V = -\dfrac{GM}{r} \)
The negative sign shows that potential decreases as we move closer to the mass.
3.2. Potential at Infinity
By convention, gravitational potential is taken as zero at infinite distance from the mass. All other values are negative.
4. Relation Between Potential and Field
The gravitational field strength is the rate at which gravitational potential changes with distance. In simple terms, the field is the 'slope' of the potential curve.
\( g = -\dfrac{dV}{dr} \)
4.1. What This Means
A steep potential curve means a strong gravitational field. A flatter curve means a weaker field.
5. Graphs of Potential and Field
Graphs help visualize how potential and field vary with distance from a mass.
5.1. Gravitational Potential vs Distance
- Potential becomes less negative as you move farther away.
- At infinity, it becomes zero.
5.2. Gravitational Field vs Distance
- Field strength decreases with \( 1/r^2 \).
- Becomes very small at large distances.