By Albert G. (ed.) Ingalls

Matters coated: Optical creation equipment and equipment Eyepieces and Small Lenses Optical Coatings and Coating apparatus the attention and surroundings different Optical tools and Instrumentation for sunlight Observations.

**Read or Download Amateur Telescope Making Book Three): A Sequel to Amateur Telescope Making Book One) and to Amateur Telescope Making Advanced Book Two PDF**

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**Additional info for Amateur Telescope Making Book Three): A Sequel to Amateur Telescope Making Book One) and to Amateur Telescope Making Advanced Book Two **

**Example text**

One sets x = r cos φ + c , y = r sin φ , and chooses the constant c so that in the equation r 2 = (x − c)2 + y 2 = [p − εr cos φ]2 = [p − ε(x − c)]2 the terms linear in x cancel. As long as ε = 1, this is achieved by the choice c= εp . e. an equation of second order containing only the squares of x and y. Here two distinct cases are possible. e. c2 > a 2 . 21 ) describes a hyperbola. The center of the force field lies at one of the foci. For the attractive case (A and p are positive) the branch of the hyperbola that opens toward the force center is the physical one.

Then x (t) ≡ x (t, s, y ) = Φ t,s (y ) = M(t, s) · y , ˜ ˜ ˜ ˜ ˜ ˜ with cos ω(t − s) sin ω(t − s) . 47) −mω sin ω(t − s) cos ω(t − s) One confirms that φ t,s and M(t, s) depend only on the difference (t − s). This must be so because˜ we are dealing with an autonomous system. It is interesting to note that the matrix M has determinant 1. We shall return to this observation later. M(t, s) = 1 mω 5 Note that the existence and uniqueness is guaranteed only locally (in space and time). Only in exceptional cases does the theorem allow one to predict the long-term behavior of the system.

Let (r, ϕ) be the polar coordinates in the plane of the orbit. 70) l dϕ . 24 Example: The Two-Body System with a Central Force 51 def Since we consider only finite orbits for which E is negative, we set B = − E. We introduce dimensionless variables by the following definitions: √ µB def def B r(t) , τ = t . 71 ) where we have set √ µB def a b= B l α .