The problem dictates:
Two punctual still masses, M₁ = 4,00·10¹²kg and M₂ = 9,00·10¹²kg, are on x₁ = 0 and x₂ = 1000m, respectively. Only the (gravitational) fields are considered.
a) Draw the fields both masses produce on P coordinate x = 500m. Calculate the resulting field, with its direction and orientation (?).
This is translated from Spanish, and the words it uses, "dirección" (direction) and "sentido" (orientation) mean exactly the same in normal Spanish, so I'm already unsure of what different things it is asking.
Beyond drawing, I'm at a loss on what to do. So I decide to check the solution because sometimes I can decipher what is meant to be done from reading it. But I still do not understand what was done this time.
The solution is:
M₁ ⃗g₁ ⃗g₂ M₂
○----------------------<-----P--------------->------------○
x=0 x=1000 m
--------------500m-------------∖------------500m----------
● Q: x = 400 m; distances between 400 m and 600 m
𝑔⃗1 = − 6,67 ⋅ 10^-11 ⋅ 4,00 ⋅ 10^12 / 500^2 = ı⃗ = −1,0672 ⋅ 10^−3ı⃗ N kg−1
𝑔⃗2 = 6,67 ⋅ 10^-11 ⋅ 9,00 ⋅ 10^12 / 500^2 = ı⃗ = 2,4012 ⋅ 10^−3ı⃗ N kg−1
𝑔⃗ (𝑃) = 𝑔⃗1 + 𝑔⃗2 = 1,334 ⋅ 10−3ı⃗ N kg−1
Its modulus is approx. 1,33 ⋅ 10−3 N kg−1, its direction is the one on the X axis, and its orientation is to the right, towards the bigger mass.
My questions:
1) What does the solution mean with "its direction is the one on the X axis"? Wouldn't that be a position?
2) What does the "Q" mean? What's there for?
3) From my understanding, the thought process was to calculate the gravitational fields of both M₁ and M₂ and then just add the results up to get the field of P. Am I correct?