I am wanting to find the height in the barometric equations below. Could anyone solve this?
Equation 1: $ {P}=P_b \cdot \left[\frac{T_b}{T_b + L_b\cdot(h-h_b)}\right]^{\textstyle \frac{g_0 \cdot M}{R^* \cdot L_b}} $
Equation 2: $ P=P_b \cdot \exp \left[\frac{-g_0 \cdot M \cdot (h-h_b)}{R^* \cdot T_b}\right] $
where
- $P_b =$ Static pressure (pascals)
- $T_b =$ Standard temperature ([[kelvin|K]])
- $L_b =$ Standard temperature lapse rate -0.0065 (K/m) in [[International Standard Atmosphere|ISA]]
- $h =$ Height above sea level (meters)
- $h_b =$ Height at bottom of layer b (meters; e.g., h_1 = 11,000 meters)
- $R^* =$ [[Universal gas constant]] for air: 8.31432 N·m /(mol·K)
- $g_0 =$ Gravitational acceleration (9.80665 m/s2)
- $M =$ Molar mass of Earth's air (0.0289644 kg/mol)