A rocket with mass of 563.17 (not including the mass of fuel) metric tons sits on the launchpad of the Kennedy Space Center (latitude 28∘31′27′′N, longitude 80∘39′03′′W ), pointing directly upwards. Two solid fuel boosters, each with a mass of 68415kg and providing 3421kN of thrust are pointed directly downwards.
The rocket also has a liquid fuel engine, that can be throttled to produce different amounts of thrust and gimbaled to point in various directions. What is the minimum amount of thrust, in kN, that this engine needs to provide for the rocket to lift vertically (to accelerate directly upwards) off the launchpad?
Assume G=6.674×10−11s3N⋅m2, and that the Earth is a perfect sphere of radius 6370km and mass 5.972×1024kg that completes one revolution every 86164s and that the rocket is negligibly small compared to the Earth. Ignore buoyancy forces.
Given constants:
- Proton mass, mp=1.67⋅10−27kg
- Neutron mass, mn=1.67⋅10−27kg
- Electron mass, me=9.11⋅10−31kg
- Avogadro's constant, N0=6.02⋅1023mol−1
- Universal gas constant, R=8.31J/(mol⋅K)
- Boltzmann's constant, kB=1.38⋅10−23J/K
- Electron charge magnitude, e=1.60⋅10−19C
- 1 electron volt, 1eV=1.60⋅10−19J
- Speed of light, c=3.00⋅108m/s
- Universal Gravitational constant,
G=6.67⋅10−11(N⋅m2)/kg2
- Solar Mass
M⊙=1.988⋅1030kg
- Acceleration due to gravity, g=9.8m/s2
- 1 unified atomic mass unit,
1u=1.66⋅10−27kg=931MeV/c2
- Planck's constant,
h=6.63⋅10−34J⋅s=4.41⋅10−15eV⋅s
- Permittivity of free space,
ϵ0=8.85⋅10−12C2/(N⋅m2)
- Coulomb's law constant,
k=4πϵ01=8.99⋅109(N⋅m2)/C2
- Permeability of free space,
μ0=4π⋅10−7T⋅m/A
- Magnetic constant,
4πμ0=1⋅10−7(T⋅m)/A
- 1 atmospheric pressure,
1atm=1.01⋅105N/m2=1.01⋅105Pa
- Wien's displacement constant, b=2.9. 10−3m⋅K
- Stefan-Boltzmann constant,
σ=5.67⋅10−8W/m2/K4