Continuing the solution:
I think the simplest way to solve it is to rearrange Equation 9 to get:
\frac{f}{1 - \phi \frac{df}{dr}} = \frac{dr/d\tau}{d\phi/d\tau} \tag{11}
Since df/dr is very small,
\frac{f}{1 - \phi \frac{df}{dr}} ≈ f \tag{12}
Then, substituting Equations 12 and 10b to...
Sir, I'm not actually sure. The only inspiration I had for imagining spiral orbits is the case of two slowly in-spiraling bodies. But now that I think about it, in that case, both bodies have a comparable gravitational effect on each other, while in this problem, the particle is assumed to have...
Thank you so much for the response, sir! I considered it when I was brainstorming for ways on how I could approach the problem. But I didn't know how I could mathematically relate r and φ to produce a general spiral orbit WHILE satisfying Equations 1 and 3.
For example, off the top of my head...
Context:
In James Hartle's Gravity, pp. 318-319, Example 15.1, he considers the case of a particle that starts falling from infinity into a Kerr black hole, initially with no kinetic energy (e = 1) and initially moving radially (ℓ = 0). The particle's motion is constrained along the equatorial...
Hi there! Thanks for responding. :D
I did approach an adviser, but all she suggested was that I work on Relativistic Astrophysics. She also supplied me with some references that I could use to study General Relativity, and told me to continue studying. The only problem is that she hasn't really...
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Hello! My name is Conclaude. I'm nineteen (19) years old, and I'm from the Philippines.
I've been studying Physics for four (4) years. Still not that experienced but willing to contribute whatever I can. So far, I'm quite fascinated with how Math just "fits in" in our physical reality.
As for...