How bright (in Watts, preferably, or lumens) is the plume from a rocket launch (e.g. a SpaceX launch)? Obviously in its direction of travel it isn't particularly bright, but what is its effective isotropic radiative power abeam?
The chemical energy from burning 1 mole (2 grams) of hydrogen in plentiful oxygen is 242 kJ. Just enough oxygen is half a mole, or 16 grams.
The Space Shuttle external tank contained 629,340 kg of liquid oxygen and 106,261 kg of liquid hydrogen. Note that this isn't enough oxygen to burn all the hydrogen, for rocket science reasons, so we'll figure out the total energy using the oxygen.
629 tonnes of LOx, or 629 million grams, is 39.3 million half-moles. At 242 kJ per half-mole, that's a total output of 9510 GJ.
The SSMEs ran for roughly 510 seconds. Dividing the energy by the time gets us 18.6 GJ/s or GW.
From the ever-useful Atomic Rockets site, I get a total thrust for the three SSMEs of 12.1 GW. Divide the useful energy, or thrust, by the total energy from burning the fuel gets an efficiency of around 65%. I remember that the SSMEs were supposed to be especially efficient, so I might guess at around 40% wasted energy for most rocket launches. Look up the thrust in megawatts for the rocket you're interested in, multiply by 40%, and divide by ten (at a guess) for the amount that goes into visible light.
Alternatively, look up the temperature of the exhaust, and work out the proportion of visible energy from a blackbody curve for that temperature. (Hint, the SSME operated at 3300°C.)
An OV-103 or also called Space Shuttle Discovery has an average lift-off mass of 2,050,000 kg.
2,050,000 kg x 9.81 = 20,110,500 N is the total weight at lift-off
The Space Shuttle Discovery has two big white solid rocket boosters on the sides and three main engines at the tail.
Thrust of both boosters is equal to 2,404,040 kg x 9.81 = 23,583,632 N
Thrust of each main engines equals to 179,097 kg x 9.81 = 1,756,942 N
Thrust of all three equals to 1,756,942 N x 3 = 5,270,826 N
Overall thrust is 23,583,632 N + 5,270,826 N = 28,854,458 N
Resultant force = thrust – weight = 28,854,458 N – 20,110,500 N = 8,743,958 N
Acceleration = resultant force ÷ mass = 8,743,958 N ÷ 2,050,000 kg = 4.27 m/s^2
The spaceship is at rest before launched, so its initial speed is 0. After one second of the launch, its speed is going to be 4.26 m/s which is going to increase as the ship accelerates. We could say that the plume from a rocket launch could be happening at the first second after the launch.
Final Answer: The energy released at such moment is (1/2) x 2,050,000 kg x (4.27 m/s)^2 = 18,688,722.5 J
Note: The amount of joules in that second equals 18,688,722.5 Watts, because J/s = Watt
I believe 18,688,722.5 J is the energy released at such moment, but it would not all convert into visible light because most of the energy is lost as heat.