Gravitational Field Explained — JAMB/WAEC Physics
A gravitational field is the region of space around a mass where its gravitational pull can be felt by another mass. It’s what causes objects to fall toward the Earth and what keeps planets in orbit.
This topic shows up regularly in JAMB and WAEC Physics, usually testing the formula for gravitational field strength and how it changes with distance. This lesson breaks it down step by step with worked examples.
Quick takeaways
- A gravitational field is the space around a mass where its gravitational force can act on another mass.
- Gravitational field strength (g) is the force per unit mass at a point in the field, measured in N/kg.
- The formula is g = GM/r², where G is the universal gravitational constant, M is the mass creating the field, and r is the distance from its center.
- Gravitational field strength decreases as distance from the mass increases — it follows an inverse-square relationship.
- On Earth’s surface, g is approximately 9.8 m/s² (or N/kg), but this value changes with altitude and on other planets.
Timestamp
- 0:00 Introduction
- 1:56 Newton’s Law of Universal Gravitation
- 4:21 Gravitational Potential
- 6:12 Conservative vs Non-Conservative Fields
- 9:42 Acceleration Due to Gravity
- 11:03 Variation of g on the Earth’s Surface
- 13:30 Mass vs Weight vs Escape Velocity
- 17:15 Parking Orbit & Weightlessness
- 19:38 Exercises
What is a gravitational field?
A gravitational field is the region surrounding a mass in which another mass experiences a gravitational force. Every object with mass creates a gravitational field around it, and the strength of that field determines how strongly it pulls on nearby objects.
The Earth’s gravitational field, for instance, is what makes objects fall to the ground and gives everything on the surface weight.
What is gravitational field strength, and how do you calculate it?
Gravitational field strength (symbol g) is defined as the gravitational force acting per unit mass at a particular point in the field. It’s calculated using:
g = GM / r²
Where:
- G = universal gravitational constant (6.67 × 10⁻¹¹ Nm²/kg²)
- M = mass of the body creating the field (e.g., Earth)
- r = distance from the center of that mass to the point being measured
This formula tells you that field strength depends on two things: how massive the object is, and how far away you are from its center.
Why does gravitational field strength decrease with distance?
Because r is squared in the denominator, gravitational field strength follows an inverse-square law – doubling the distance from a mass reduces the field strength to a quarter of its original value, not half.
This is why astronauts in orbit still experience some gravity, just much weaker than at the Earth’s surface, and why gravitational pull becomes negligible at very large distances.
How do you answer gravitational field questions in JAMB and WAEC?
Most exam questions fall into one of these patterns:
- Direct substitution – given G, M, and r, calculate g
- Comparative questions – comparing field strength at two different distances or on two different planets
- Conceptual questions – explaining why g changes with height or differs between planets
The key mistake students make is forgetting that r is measured from the center of the mass, not from its surface so “height above the surface” must be added to the planet’s radius before applying the formula.
Common mistakes students make with gravitational field
- Using height above the surface instead of total distance from the center in the formula
- Forgetting to square r, which changes the answer significantly
- Confusing gravitational field strength (g) with gravitational force (F) – they’re related but not the same thing
- Mixing up units (N/kg vs m/s²), though numerically they are equivalent
Frequently asked questions
Q: What is the formula for gravitational field strength?
Gravitational field strength is given by g = GM/r², where G is the universal gravitational constant, M is the mass of the object creating the field, and r is the distance from its center.
Q: Why does gravitational field strength decrease as you move away from Earth?
Because the relationship follows an inverse-square law – as distance r increases, field strength decreases much faster than a simple 1:1 ratio, since r is squared in the formula.
Q: Is gravitational field strength the same as gravitational force?
No. Gravitational field strength is the force acting per unit mass at a point, while gravitational force depends on both masses involved and is calculated using Newton’s law of universal gravitation.
Q: What is the value of Earth’s gravitational field strength?
At the Earth’s surface, gravitational field strength is approximately 9.8 N/kg (equivalent to 9.8 m/s²), though this value decreases slightly with altitude.
This is one topic from our full JAMB & WAEC Physics course — see everything covered →
Lesson by Samuel Atusiuba, 3 years of experience teaching JAMB & WAEC Physics.
