Missile like targeting

Hello, I want to create a missile like targeting system. I have tried this using bodymovers and then updating the position with runservice.

This is what the code currently looks:

local missile = script.Parent  -- The missile part
local target = workspace.Target   -- The target part
local up_speed = 50 -- The speed at which the missile goes up
local fly_speed = 750 -- The speed at which the missile flies towards the target

-- Constants
local GRAVITY = 196.2  -- The gravity constant in Roblox (studs/s^2)
local TIME_STEP = 0.0167  -- The time step used in the RunService.Heartbeat event (seconds)

-- Create BodyMovers
local bv = Instance.new("BodyVelocity")
bv.MaxForce = Vector3.new(math.huge, math.huge, math.huge)
bv.Velocity = missile.CFrame:vectorToWorldSpace(Vector3.new(0, up_speed, 0))
bv.P = 5000
bv.Parent = missile

local bf = Instance.new("BodyForce")
bf.Force = Vector3.new(0, -missile:GetMass() * GRAVITY, 0)
bf.Parent = missile

	if (missile.Position - target.Position).magnitude <= 10 then

	-- Calculate the new velocity of the missile
	local dir = (target.Position - missile.Position).unit
	local vel = dir * fly_speed

	-- Update the BodyMovers
	bv.Velocity = Vector3.new(0, bv.Velocity.Y, 0)
	bf.Force = Vector3.new(0, -missile:GetMass() * GRAVITY, 0) + missile.CFrame:vectorToWorldSpace(Vector3.new(0, 0, -vel.magnitude * missile:GetMass()))


I want it to go up and then curve to the target while moving, like real missiles do.

I did a quick search and found this:

I think you should use lineforce as it would always go towards the attachmentposition also use a bodyforce and set the force of y to part.mass*workspace.gravity this will make sure that gravity doesnt effect the part