Gravitational Field Strength of a point in between Two Planets

Question

In my textbook, under the topic of gravitation,  it states that if the centres of 2 planets, each of mass $M$ and separated by a distance $r$ and you have  a point halfway between the centres of the planets, the gravitational field strength at that point is $0$.
I don't fully understand why that is. Is it because the point feels an equal force in each direction so the resultant gravitational force is $0$, resulting in $0$ gravitational field strength at that point?
Surely however gravitational field strength is a measure of how many Newtons of gravitational force a body feels per kg. In this case, shouldn't it be equal to
$$2times frac{GM}{(0.5r)^2}=frac{8GM}{r^2}$$
as it feels
$frac{GM}{(0.5r)^2}$ Newtons of force from 2 planets?

sammy gerbil · Accepted Answer

You are correct. The two forces are in opposite directions and cancel each other.
Force is a vector quantity. When adding vectors the directions are as important as the magnitudes.
Perhaps you are confusing gravitational field strength $g=GM/r^2$ and gravitational potential $V=-GM/r$. The former is gravitational force per unit mass, so like force it is a vector. When adding field strength you use vector addition (eg the parallelogram rule). The latter is the work done in moving a unit mass from infinity to a point at distance $r$ from the mass $M$, so like work it is a scalar. When adding potentials due to several masses you do so algebraically, regardless of the direction of the mass which is creating the potential.

Gravitational Field Strength of a point in between Two Planets

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