Physics & astronomy toolkit

1. 2D vector addition
2. Universal gravitational force
3. Relativistic Lorentz dilation & E=mc²
4. Pendulum period (simple & large amplitude)
5. Barometric altitude & pressure
6. STP & SATP molar volume
7. Electron subshell configuration
8. Isotope radioactive decay
9. Kepler's 3rd law orbital period
10. Schwarzschild black hole radius
11. Planetary synodic alignment
12. Scale solar system modeller

$$R_x=\sum F_i\cos\theta_i,\quad R_y=\sum F_i\sin\theta_i,\quad|R|=\sqrt{R_x^2+R_y^2}$$

Enter up to 6 magnitude/angle pairs. Source: 1728 Software Systems.

$$F=G\frac{m_1m_2}{r^2},\quad G=6.67430\times10^{-11}\ \text{m}^3\text{kg}^{-1}\text{s}^{-2}$$

$$\gamma=\frac{1}{\sqrt{1-v^2/c^2}},\quad t'=\gamma t,\quad L'=\frac{L}{\gamma},\quad E=mc^2$$

$$T_0=2\pi\sqrt{\frac{L}{g}},\quad T=T_0\!\left[1+\frac{1}{4}\sin^2\!\frac{\theta_0}{2}+\frac{9}{64}\sin^4\!\frac{\theta_0}{2}+\cdots\right]$$

$$P(h)=P_0\!\left(1-\frac{Lh}{T_0}\right)^{\!gM/RL},\quad R=287\ \text{J/kg·K},\ L=0.0065\ \text{K/m}$$

$$V_m=\frac{RT_{\text{std}}}{P_{\text{std}}},\quad R=8.314462\ \text{J/mol·K}$$

IUPAC pre-1982: 0°C/1 atm. Post-1982: 0°C/100 kPa. NIST NTP: 20°C/1 atm. SATP: 25°C/100 kPa.

Generates electron configuration for elements Z=1–118. Order: 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d 7p.

$$A(t)=A_0(1/2)^{t/t_{1/2}},\quad\lambda=\ln 2/t_{1/2}$$

$$T^2=\frac{4\pi^2}{GM}a^3,\quad v_{\text{orb}}=\sqrt{\frac{GM}{a}}$$

$$r_s=\frac{2GM}{c^2},\quad c=2.99792458\times10^8\ \text{m/s}$$

$$\frac{1}{S}=\left|\frac{1}{P_1}-\frac{1}{P_2}\right|$$

Time between successive conjunctions of two planets.

Scale planetary dimensions to a user-defined Sun diameter. Enter Sun's scaled size.