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I am curious on what are those multiple connection cables latched between the rocket and launch pad.

What exactly is the purpose of it, I am aware that one should be for filling up the fuel. But what are the rest used for, and I wonder what makes those connections so crucial that they are not disconnected until the lift off.

Please refer the picture Atlas V

enter image description here

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    $\begingroup$ Don’t forget that all the fluids and gases that went in might have to come back out if the launch is scrubbed. You don’t want to have to send somebody out to replug umbilicals into a fully-fueled rocket just because you unplugged them too soon before a scrubbed launch. $\endgroup$ Mar 13 '19 at 19:20
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In general, umbilicals are provided from the launch pad to the vehicle for any services that need to be provided after the vehicle is installed on the launch mount, and to remove hazardous gases from the vicinity of the vehicle.

Consider that vehicles can sit on the pad for long periods if problems occur during the countdown. Many different consumables may need to be replenished. Use of ground supplied power and cooling conserves vehicle resources for flight.

Details vary, but will be similar for all vehicles.

enter image description here

For the Space Shuttle, the top umbilical arm (the "beanie cap") connected to the liquid oxygen tank vent at the tip of the External Tank, and carried oxygen vapors away from the vehicle.

The next arm down, which passes on the other side of the solid rocket booster in this picture, is the External Tank Hydrogen Vent and Intertank Access Arm...which does exactly as its name suggests.

The next arm down is the Crew Access Arm.

Most interfacing services on the Shuttle were provided by the Tail Service Masts, the gray tombstone-shaped structures to the left and right of the Orbiter tail. They supplied cold coolant, purge gas, liquid oxygen, liquid hydrogen, gaseous nitrogen and gaseous helium, and returned warm coolant, recirculated liquid oxygen and liquid hydrogen to the ground facilities. Sense line connections for the leak detection system were provided. They also supplied connections for electrical power, communications, and data.

Here is a schematic of one of the T-0 umbilicals showing the various connectors and a list of the services provided through them. I haven't found a list for the other umbilical but it was very similar.

enter image description here

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Source

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    $\begingroup$ Nice answer! Would it be worth including a Saturn V picture to show how many umbilicals might be necessary without something like the Tail Service Masts? $\endgroup$
    – DylanSp
    Mar 13 '19 at 15:53
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    $\begingroup$ I really wonder how much they could be reduced nowadays with wireless data transfer being reliable and ubiquitous and only resources/waste needing transfer. $\endgroup$
    – SF.
    Mar 13 '19 at 16:24
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    $\begingroup$ @OrganicMarble In my experience wireless is always a failure point ;-). $\endgroup$ Mar 13 '19 at 18:54
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    $\begingroup$ I've a suspicion no-one is using wireless telemetry on the pad, beyond ensuring the link is operational as go-no-go step. But modern technologies like ethernet replace a lot of wiring to analog sensors. $\endgroup$
    – Saiboogu
    Mar 13 '19 at 20:31
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    $\begingroup$ @PeterA.Schneider: In my experience connections are always a failure point and wireless fails no more often than physical. Especially where mechanical stresses are involved, wireless tends to deal with them better. $\endgroup$
    – SF.
    Mar 14 '19 at 10:26

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