**We’re covering:**

- Gravitational Field Strength
- Radii of Planets (R)
- Graph of g against r
- Acceleration of Free Fall

**Let’s go!**

__What is Gravitational Field Strength?__

Force per unit mass acting on a small mass placed at a point in the field.

**We denote this as a lowercase g.**

g = F/m

Since F = GMm/r^{2},

**g = G****M****/r**^{2}

Note that the ‘m’ has disappeared!

- g is INDEPENDENT of the smaller test mass.
- g is the same for 2 small objects at an equal distance from the large mass (M),

even if they have different masses (m_{A} & m_{B}).

Also note that F = ma

g = F/m = a

Thus,

**g has a unit of acceleration (ms**^{-2}).

__Radii of Planets!__

When talking about large masses such as planets, we must remember to differentiate between the DISTANCE TO THE CENTRE (r) & the HEIGHT (h).

**A bit of notation:**

- r = Distance between larger & smaller point mass
- R = radius of planet
- h = height above planet (altitude)

**Thus, you can calculate r with:**

r = height of m above the surface + radius of planet

r = R + h

__For example:__

A satellite orbits at 1000 km above the Earth.

The Earth’s radius is 6.4 x 10^{6} m

For calculations, use

r = h + R

R = 1.0 x 10^{6} + 6.4 x 10^{6
}R = 7.4 x 10^{6 }m

__How does g vary with distance from the centre of a large mass?__

**Below the surface** |
g increases as distance increases.
g ∝ r
This is because as you travel further towards the surface, there is MORE MASS beneath you.
The larger mass exerts a stronger gravitational force.
Below the surface, remember that the point mass is NOT the same as M above the surface. |

**On (near) the surface** |
g is proportional to the mass, & inversely proportional to the square of the radius of the planet.
g = GM/R^{2}
For small changes in height near the surface, g is approximately constant (see below). |

**Above the surface** |
g is proportional to the mass, & inversely proportional to the square of the distance to the centre of the planet.
g = GM/r^{2
}g = GM/(R + h)^{2} |

__Field Strength on the Surface of a Planet__

g changes noticeably when r changes by a large amount (multiple kilometres),

For small changes in height near a planet’s surface (few metres), the change in g is negligible.

Thus, we can approximate field strength to be constant near the surface.

Since g is in units of acceleration, we also call it the **acceleration of free fall**.

On Earth, g = 9.81 ms^{-2}.

**⇐ Previous in Physics: Gravitational Fields & Force**

**⇒ Next in Physics: Circular Orbits**

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