Gravitational Field Formula

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

The Formula

g=Fm=GMr2g = \frac{F}{m} = \frac{GM}{r^2}

When to use: A planet creates an invisible pull around it. The closer you are, the stronger that pull is.

Quick Example

Near Earth's surface, the gravitational field strength is about 9.89.8 N/kg, which is why a 1 kg object weighs about 9.89.8 N.

Notation

gg is gravitational field strength in N/kg or m/s2^2, FF is force, mm is the test mass, GG is the gravitational constant, and rr is distance from the source centre.

What This Formula Means

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

A planet creates an invisible pull around it. The closer you are, the stronger that pull is.

Formal View

The gravitational field strength is g⃗=F⃗/m\vec{g} = \vec{F}/m. For a spherical mass MM, the field magnitude at distance rr is g=GM/r2g = GM/r^2, directed toward the centre of the mass.

Worked Examples

Example 1

medium
Find the height above Earth's surface where gg drops to 4.9 N/kg4.9\,\text{N/kg}. Use R=6.4×106 mR = 6.4\times 10^6\,\text{m}, gsurf=9.8 N/kgg_{surf} = 9.8\,\text{N/kg}.

Answer

h≈2.65×106 mh \approx 2.65\times 10^6 \text{ m}

First step

1
g/gsurf=(R/r)2=0.5g/g_{surf} = (R/r)^2 = 0.5, so r/R=2r/R = \sqrt{2}.

See the full worked solution + why-it-works coaching

SetupKey insightWhy it worksCommon pitfallConnection

Unlock answer keys One Family plan — every worked solution, all subjects

Example 2

hard
Inside a uniform-density planet (mass MM, radius RR), the field at radius r<Rr < R is g(r)=GMr/R3g(r) = GMr/R^3. Find the depth below the surface where gg equals half its surface value.

Example 3

hard
At Earth's surface a person weighs 700 N700\,\text{N}. The same person stands on a tower at altitude h=2.0×106 mh = 2.0\times 10^6\,\text{m}. Find their weight there. Use RE=6.4×106 mR_E = 6.4\times 10^6\,\text{m}.

Common Mistakes

  • Confusing gravitational field strength gg with the universal constant GG. - Fix this by naming the system, checking "Have I isolated one system and listed the external forces or torques acting on it before applying a law?", and attaching units or direction to the final statement.
  • Using surface distance instead of centre-to-centre distance in GM/r2GM/r^2. - Fix this by naming the system, checking "Have I isolated one system and listed the external forces or torques acting on it before applying a law?", and attaching units or direction to the final statement.
  • Using gravitational field from a keyword alone - Signal words like force, push, pull only point to a possible model; the system must match too.
  • Substituting numbers before defining the system - A formula cannot repair a missing object, boundary, direction, medium, or circuit path.

Why This Formula Matters

Gravitational Field is central because forces explain changes in motion and balance. Students who can isolate a system and draw the interactions can avoid treating every force word as the same kind of cause.

Frequently Asked Questions

What is the Gravitational Field formula?

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

How do you use the Gravitational Field formula?

A planet creates an invisible pull around it. The closer you are, the stronger that pull is.

What do the symbols mean in the Gravitational Field formula?

gg is gravitational field strength in N/kg or m/s2^2, FF is force, mm is the test mass, GG is the gravitational constant, and rr is distance from the source centre.

Why is the Gravitational Field formula important in Physics?

Gravitational Field is central because forces explain changes in motion and balance. Students who can isolate a system and draw the interactions can avoid treating every force word as the same kind of cause.

What do students get wrong about Gravitational Field?

Students often know a formula related to gravitational field but skip the recognition step: Have I isolated one system and listed the external forces or torques acting on it before applying a law? That leads to a correct-looking substitution attached to the wrong physical model.

What should I learn before the Gravitational Field formula?

Before studying the Gravitational Field formula, you should understand: gravity, mass.

← Back to Gravitational Field See All Examples Practice Problems