- #1
AdrianGriff
- 21
- 0
So this should be coming easily, but for some reason I can't seem to grasp why or how this is being done:
So say we have equation:
0 = a + (μ/r3) r , where μ = G(M+m) or ≈ GM and M >> m.
According to this book, the first step to finding ξ, the Specific Mechanical/Orbital Energy they dot multiplied the vector v through the equation above like so:
v ⋅ a + v ⋅ (μ/r3) r = 0
And just below that, there is:
va + (μ/r3) rv = 0
So basically, my question is:
Why do all the vectors turn into scalars, considering that the dot product cannot actually be performed because we do not know the components of those variable vectors?
Should it not just stay as the equation with vectors?
Or why does a ⋅ v not equal a1v1 + a2v2?
Thank you!
- Adrian
So say we have equation:
0 = a + (μ/r3) r , where μ = G(M+m) or ≈ GM and M >> m.
According to this book, the first step to finding ξ, the Specific Mechanical/Orbital Energy they dot multiplied the vector v through the equation above like so:
v ⋅ a + v ⋅ (μ/r3) r = 0
And just below that, there is:
va + (μ/r3) rv = 0
So basically, my question is:
Why do all the vectors turn into scalars, considering that the dot product cannot actually be performed because we do not know the components of those variable vectors?
Should it not just stay as the equation with vectors?
Or why does a ⋅ v not equal a1v1 + a2v2?
Thank you!
- Adrian
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