Understand gravitational fields the easy way, with plain English intuition, an interactive simulation, the inverse square law, worked examples and an auto marked practice test. VCE Physics Units 3 and 4.
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Hold a ball above the ground, let go, and it falls. Something invisible reached out and pulled it down. That something is a gravitational field, the region of space around any mass where another mass feels a pull toward it. Every mass makes one, and the bigger the mass, the stronger the pull. The whole of this topic is really just two short formulas describing how strong that pull is and which way it points.
What a field actually is
A gravitational field is simply the region where a mass feels a force. You cannot see it, but you can map it. Put a small test mass anywhere near a planet and it gets tugged toward the planet. Do that everywhere and you build up a picture of arrows all pointing inward, and that picture is the field.
The strength of the field at a point is called the gravitational field strength, written g, and it is measured in newtons per kilogram (N/kg). It tells you how many newtons of pull each kilogram of mass would feel if you placed it there.
g=r2GM
Here M is the mass making the field, r is the distance from the centre of that mass, and G=6.67×10−11 is the gravitational constant, a fixed number that never changes. At Earth’s surface this works out to g=9.8 N/kg, the number you have used since junior science.
The grey arrows are the field, all pointing inward toward the mass. Notice they are packed tightly near the planet and spread apart further away. That spreading is the picture of the field getting weaker with distance. The red arrow is the force that a real test mass m feels when it sits on one of those field lines.
From field strength to force
Once you know the field strength g at a point, finding the force on an object is easy. The field strength already tells you the pull per kilogram, so you just multiply by how many kilograms you have.
F=mg
Spell that out using the field formula and you get the full gravitational force law:
F=r2GMm=mg
Both forms say the same thing. Use F=mg when you already know the field strength, and use F=r2GMm when you are working straight from the two masses and their separation.
See it for yourself
Slide the two masses closer and further apart and watch the force arrows grow and shrink. Notice how quickly the pull falls away as the separation grows, because the field follows an inverse square law.
To find the field strength, use g=r2GM with the mass M making the field and the distance r from its centre.
Always square the radius in the bottom line. This is the most common slip.
To find the force on a mass, use F=mg with the field strength of the body you are standing on.
Keep everything in scientific notation so the powers of ten stay tidy.
Remember the inverse square rule. Doubling the distance does not halve the field, it makes it one quarter as strong.
Lock it in with active recall
Cover the answer and say each one out loud before you flip. Rate yourself honestly — the cards you find hard come back sooner, the ones you know are spaced further out.
Active recall
Answer from memory first, then flip. Rate yourself and each card returns on a spaced schedule (1 → 3 → 7 → 16 days).
Write the formula for gravitational field strength and name each symbol.
g=r2GM — M is the source mass, r the distance from its centre, G=6.67×10−11 the gravitational constant.
What are the units of gravitational field strength g?
Newtons per kilogram (N/kg) — the pull each kilogram of mass would feel at that point.
Move from a distance r to 2r from a planet. What happens to g?
It drops to one quarter, because g∝r21 and 221=41.
Once you know the field strength g, how do you find the force on a mass m?
F=mg — equivalently F=r2GMm. The force points toward the source mass.
Does a heavier object sit in a stronger gravitational field?
No. The field strength g depends only on the source mass and your distance from it, not on the object placed there. A heavier object feels a bigger force, but the field is the same.
Recall · Electric Fields
What is the field around a single point charge, and how does it change with distance?
E=r2kQ — also an inverse square law, so doubling the distance drops the field to a quarter, exactly the same shape as gravity.
Recall · Satellites and Orbits
Why does a satellite’s orbital speed not depend on its own mass?
Setting gravity equal to the centripetal force, r2GMm=rmv2, the satellite mass m cancels, leaving v=rGM.
See the recipe in action in the Worked Examples tab, then test yourself in Try It.
Worked examples
Worked Example 1Field strength at a planet's surface
A planet has mass 6.0×1024 kg and radius 6.4×106 m. Taking G=6.67×10−11, find the gravitational field strength at its surface.
1
Field strength is set by the mass making the field and how far you are from its centre. Write down the formula.
g=r2GM
2
Substitute the mass, the radius and the constant G. Keep everything in scientific notation.
g=(6.4×106)2(6.67×10−11)(6.0×1024)
3
Work out the top line and the bottom line separately.
g=4.096×10134.0×1014
4
Divide to get the field strength in newtons per kilogram.
g=9.8 N/kg
Answer
g=9.8 N/kg
Worked Example 2Force on a person standing there
A 50 kg person stands on the surface of that same planet, where g=9.8 N/kg. Find the gravitational force on the person.
1
The force on a mass is just its mass multiplied by the field strength it sits in.
F=mg
2
Substitute the mass and the field strength.
F=50×9.8
3
Multiply to get the force in newtons.
F=490 N
Answer
F=490 N
Practice questions
Practice test
Try it yourself
6 questions, 9 marks
Choose your answers, then submit to see your score and the full worked solutions.
Multiple choice is marked for you, just like Exam 2 Section A.
Q1.The gravitational field around a point mass is best described as:
1mark
Need a hint?
Gravity always pulls toward the mass, and it is an inverse square field.
Show worked solution
A gravitational field always points toward the mass that makes it, so the field lines run radially inward. Because g=r2GM, the strength falls off as the square of the distance, so the field gets weaker as you move away. Outward field lines describe a repulsion, which gravity never does.
Q2.A planet has mass 2.0×1024 kg and radius 4.0×106 m. Using G=6.67×10−11, the gravitational field strength at its surface is closest to:
1mark
Need a hint?
Use g=r2GM and remember to square the radius.
Show worked solution
g=r2GM=(4.0×106)2(6.67×10−11)(2.0×1024)=1.6×10131.334×1014=8.3 N/kg. Forgetting to square the radius is the classic slip and gives a much larger number.
Q3.At the surface of a moon the gravitational field strength is 2.0 N/kg. The gravitational force on a 30 kg rock resting on the surface is:
1mark
Need a hint?
Use F=mg with the field strength of the moon, not Earth.
Show worked solution
F=mg=30×2.0=60 N. Option D uses Earth's 9.8 N/kg by mistake. Always use the field strength of the body you are actually standing on.
Q4.A satellite is moved from a distance r to a distance 2r from the centre of a planet. The gravitational field strength it experiences becomes:
1mark
Need a hint?
The field is an inverse square field, so double the distance changes g by a factor of 221.
Show worked solution
Because g∝r21, doubling the distance divides the field strength by 22=4. So the field becomes one quarter as strong. This inverse square behaviour is why field lines spread further apart with distance.
Q5.A planet has mass 1.2×1025 kg and radius 1.0×107 m. Taking G=6.67×10−11, find the gravitational field strength at its surface. Show your working.
3marks
Work this on paper. The worked solution appears once you submit.
Show worked solution
Use the field strength formula with the mass and radius given.
g=r2GM=(1.0×107)2(6.67×10−11)(1.2×1025).
The top line is 8.0×1014 and the bottom line is 1.0×1014, so
g=1.0×10148.0×1014=8.0 N/kg.
Q6.To find the work done lifting a 500 kg spacecraft from Earth's surface to an altitude of 250 km, Tom writes W=mgΔh=500×9.81×250000=1.23×109 J. Ignoring air resistance, identify the assumption Tom has made in using this formula, and state its effect on his value of W.
2marks
Work this on paper. The worked solution appears once you submit.
Show worked solution
Tom assumes the gravitational field strength g stays constant at its surface value. In reality g decreases with altitude (since g=r2GM), so the true average force is smaller. Using the surface value of g therefore overestimates the work done.
VCAA 2025 Physics Exam, Section B Q9
Frequently asked questions
What is the difference between field strength g and force F?
Field strength g (in N/kg) describes how strong the field is at a point, before any object is put there. Force F (in N) is what an actual mass m feels once it sits in that field, and F equals m times g.
Why do the field lines get further apart with distance?
Gravity is an inverse square field, so g equals GM divided by r squared. Doubling the distance makes the field one quarter as strong, and the spreading out of the field lines is the picture of that weakening.
Does a heavier object sit in a stronger gravitational field?
No. The field strength g at a point depends only on the mass making the field and your distance from it, not on the object placed there. A heavier object feels a bigger force, but the field itself is the same.
