if the radial and transverse velocities of a point are always proportional to each other and this hold for acceleration also prove that its velocity will vary as sime power of the radius vector
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Step-by-step explanation:
The radial and transverse components which they are moving rapidly with an outward direction.
Where the radial velocity is an object for the path from a fixed point through a straight line.
And the transverse velocity which will refers to an object to a path with an angle θ to the origin path from a fixed point.
radical velocities ∝ transverse velocities
dr/dt ∝ r dθ/dt
dr/dt ∝ λr dθ/dt
Where λ is constant
dr/r = λ dθ
By integrating we get
log r = λθ + log a where log a is constant
Where
log r - log a = λθ
log r/a = λθ
r/a = e^{λθ}
r = ae^{λθ}
Hence it is an equiangular spiral
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