Launch vehicles using mobile launch pads have many umbilical connections, whereas the ones using TEL launch structure with strongback, don't. Why is that?
As seen in the picture, Electron has just one main umbilical:
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Let's look at what umbilicals are on SLS, a fairly traditional and very large rocket. It has two stages and two boosters and a crewed capsule. It uses cryogenic liquid oxygen and hydrogen for fuel.
Two aft skirt electrical umbilicals, or ASEUs, will connect to the SLS rocket at the bottom outer edge of each booster and provide electrical power and data connections to the SLS rocket until it lifts off from the launch pad. The ASEUs will act like a telephone line and carry a signal to another subsystem on the mobile launcher called the Launch Release System.
Two aft skirt purge umbilicals, or ASPUs, also will connect to the SLS rocket at the bottom outer edge of each booster to remove potentially hazardous gases and maintain temperature range of components through a heated gaseous nitrogen purge to the cavity of each booster’s aft skirt
Two tail service mast umbilicals, or TSMUs, will connect from the zero-level deck on the mobile launcher to the SLS rocket core stage aft section. The TSMUs are about 33 feet tall. They will provide liquid oxygen and liquid hydrogen fluid lines and electrical cable connections to the SLS core stage engine section to support propellant handling during prelaunch operations.
The core stage inter-tank umbilical, or CSITU, is a swing arm umbilical that will connect to the SLS core stage inter-tank. The inter-tank umbilical’s main function is to vent gaseous hydro-gen from the core stage. The arm also provides conditioned air, pressurized gases and power and data connection to the core stage.
The core stage forward skirt umbilical, or CSFSU, is located at the 180-foot level on the mobile launcher tower, above the liquid oxygen tank. The CSFSU is an umbilical that will swing into position to provide connections to the core stage forward skirt of the SLS rocket, and then swing away before launch. CSFSU’s main purpose is to provide conditioned air/GN2 to the SLS Core Stage Forward Skirt cavity.
The interim cryogenic propulsion stage umbilical, or ICPSU, is located at about the 240-foot level on the mobile launcher tower. The swing arm ICPSU will supply fuel, oxidizer, environmental control systems, pneumatics and electrical connections to the interim cryogenic propulsion stage of the SLS rocket.
The Orion service module umbilical, or OSMU, will connect from the mobile launcher tower to the Orion service module. The umbilical is located at the 280-foot level of the tower and, prior to launch will transfer liquid coolant for the elec-tronics and air for the electronics and purge air/GN2 for the environmental control system to support the spacecraft.
The crew access arm, or CAA, is located at the 274-foot level on the mobile launcher tower. The CAA will rotate from its retracted position and interface with the SLS rocket at the Orion crew hatch location to provide entry in and exit from the Orion crew module. It will provide a safe and unobstruct-ed pathway for entry and exit during processing operations in the Vehicle Assembly Building, and processing and launch operations at Launch Pad 39B.
The vehicle stabilizer system, or VSS, is located at the 200-foot level of the mobile launcher tower, and will provide a structural interface to the SLS core stage. The VSS will help reduce core stage vehicle motion during rollout to the launch pad, process-ing operations, high wind events at the pad, and the launch countdown.
Electron has two stages with no boosters and an uncrewed payload. It uses non-cryogenic RP-1 (liquid kerosene) and liquid oxygen (LOX) as its fuels.
Without the boosters nor a crewed payload module, that leaves just these equivalent umbilicals to supply the SLS core.
Unfortunately I don't have details of what's in the Electron umbilical, but we can make a few guesses.
With the Electron rocket being so much smaller, it doesn't need a dedicated stabilizer.
While both Electron and SLS use cryogenics, LOX has a much higher boiling point than the liquid hydrogen used on the SLS. And the much simpler Electron can be stacked and rolled out much faster than the huge and complex SLS, so it spends less time sitting on the pad heating up. The SLS carries 80 tons of fuel, the Electron about 10 tons. It doesn't need as much cryogenics while sitting on the pad, if at all.
With the reduced fuel, reduced size, less need for cryogenics, modern data architecture of the Electron it's not unreasonable that yes, they can compress the three remaining core umbilicals into one.