include Math
m_start = 10000.0
v_start = 371e3
v_exh = 18e3
m_prop = 540.0
m_end = m_start - m_prop
delta_v = v_exh*log(m_start/m_end)
v_end = v_start + delta_v
# Note simplification here: the propellant ends up with a range of velocities spread across ~1 km/s.
# Take the midpoint of the range, which is not exactly correct, but close.
v_prop_end = v_start - v_exh + 0.5*delta_v
ke_start = 0.5*m_start*v_start**2/1e9
ke_end = 0.5*m_end*v_end**2/1e9
ke_prop_end = 0.5*m_prop*v_prop_end**2/1e9
puts
puts "v_start: #{v_start}"
puts "v_end: #{v_end}"
puts "ke_start: #{ke_start}"
puts "ke_end: #{ke_end}"
puts "ke_prop_end: #{ke_prop_end}"
puts "difference: #{ke_end + ke_prop_end - ke_start}"
e_engine = 0.5*m_prop*v_exh**2/1e9
puts "e_engine: #{e_engine}"