That is the mystery. In Tantra Jyotisha, Ketu is given to Dhumavati in the Dasa Mahavidya Yet Vinayaki also holds Ketu in the ashtamatrika (saptamatrika), because she emerges as the Shakti of Ganesha, some texts mention Narasimhi from Narasimha and others Vinayaki from Ganesha.In the assembly of planets, Ketu is associated with Shree Ganesha.
Same planet. Two different initiations.
The Widow Who Remains
Dhumavati is Ketu as the void after the fire.
Smoky, old, widowed, riding a crow with winnowing basket, she gives no comfort. She is the Mahavidya who teaches through removal. Husband gone, jewels gone, sweetness gone. What remains when all that defined you is gone? That is her prasad.
Astrologically this is Ketu as detachment, past karma, sudden loss, the house where you feel strangely uninterested even when the world says you should want. Her gift is terrible and clean. She severs fascination.
The Mother Who Blocks
Vinayaki is Ketu as the threshold.
Elephant headed, vermillion, broad bellied, she is the forgotten Matrika, the feminine Ganesha. Where Dhumavati is emaciated by loss, Vinayaki is corpulent with digestion. She holds experience in her belly until it becomes wisdom.
Among the planets, Ganesha is most associated with Ketu, the south node of the Moon, the headless tail of the serpent. Vinayaki inherits that Ketu, but as guardian rather than ghost. She places the obstacle, she removes the obstacle. She is the intelligence that says not yet, not this door.
One Ketu, Two Doors
In esoteric terms, you could say Ketu has a dissolving current and a guarding current.
Dhumavati dissolves the head. She leaves you headless like Ketu itself, wandering through the smoke of what was. No plan works. That is the teaching.
Vinayaki replaces the head. Like Ganesha, whose human head was cut and replaced with an elephant’s, she gives you a larger head, a subtler perception that can sense karmic knots before you blunder into them.
One is the Ketu of the cremation ground. The other is the Ketu of the temple doorway.
In Sadhana
Turn to Dhumavati when Ketu comes as emptiness. When grief has no object, when success feels tasteless, when you are widowed from your own ambition. Do not ask her to fix it. Ask her to let the smoke teach.
Turn to Vinayaki when Ketu comes as blockage. When beginnings stall, when a path loops back on itself, when you need not transcendence but right entry. She does not remove you from the world. She teaches you how to enter it without being devoured.
The widow and elephant mother are not rivals. They are two hands of the same shadow, one opening to the void, one pressing into form.