# Newtonian Mechanics – Gravitational Field Strength of a Point in Between Two Planets

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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
$$2\times \frac{GM}{(0.5r)^2}=\frac{8GM}{r^2}$$
as it feels
$$\frac{GM}{(0.5r)^2}$$ Newtons of force from 2 planets?

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.