User:JohnOwens/Orbital equations

From Wikipedia, the free encyclopedia

Contents

Variables

Time-related

  • ω angular velocity
  • N rotational speed
  • T time (of period)

Distance-related

  • r radius
  • v velocity (tangential)
  • a acceleration
    • ac centripetal acceleration

Gravitational

  • MG product of central or total mass and gravitational constant

Cumulative equations

  1. \omega \equiv 2\pi N
  2. \omega T \equiv 2\pi
  3. N T \equiv 1
  4. \omega r \equiv v
  5. \omega^2 r \equiv a
  6. ω2r3 = MG
  7. ωv = a
  8. ωMG = v3
  9. ω4MG = a3
  10. Tv = 2πr
  11. T2a = 4π2r
  12. T2MG = 4π2r3
  13. Ta = 2πv
  14. Tv3 = 2πMG
  15. T4a3 = 16π4MG
  16. 2πNr = v
  17. 4π2N2a = r
  18. 4π2N2r3 = MG
  19. 2πNv = a
  20. 2πNMG = v3
  21. 16π4N4MG = a3
  22. r a \equiv v^2
  23. rv2 = MG
  24. a r^2 \equiv MG
  25. v4 = aMG

Isolated variable equations

Time-related

ω

  1. \omega \equiv {2 \pi \over T} \equiv 2 \pi N
  2. \omega = {v \over r}
  3. \omega = {a \over v}
  4. \omega = \sqrt{a \over r}
  5. \omega = {v^3 \over MG}
  6. \omega = \sqrt{MG \over r^3}
  7. \omega = \sqrt[4]{a^3 \over MG}

N

  1. N \equiv {\omega \over 2\pi} \equiv {1 \over T}
  2. N = {v \over 2\pi r}
  3. N = {a \over 2\pi v}
  4. N = {\sqrt{r} \over 2\pi\sqrt{a}} \equiv \sqrt{r \over 4\pi^2a}
  5. N = {v^3 \over 2\pi MG}
  6. N = {\sqrt{MG} \over 2\pi\sqrt{r^3}} \equiv \sqrt{MG \over 4\pi^2r^3}
  7. N = {\sqrt[4]{a^3 \over MG} \over 2\pi} \equiv \sqrt[4]{a^3 \over 16\pi^4 MG}

T

  1. T \equiv {2\pi \over \omega} \equiv {1 \over N}
  2. T = {2\pi r \over v}
  3. T = {2\pi v \over a}
  4. T = 2\pi\sqrt{r \over a} \equiv \sqrt{4\pi^2 r \over a}
  5. T = {2\pi MG \over v^3}
  6. T = 2\pi\sqrt{r^3 \over MG} \equiv \sqrt{4\pi^2 r^3 \over MG}
  7. T = 2\pi\sqrt[4]{MG \over a^3} \equiv \sqrt[4]{16\pi^4 MG \over a^3}

Distance-related

r

  1. r = {v \over \omega} \equiv {v \over 2\pi N} \equiv {T v \over 2\pi}
  2. r = {a \over \omega^2} \equiv {a \over 4\pi^2 N^2} \equiv {T^2 a \over 4\pi^2}
  3. r = \sqrt[3]{MG \over \omega^2} \equiv \sqrt[3]{MG \over 4\pi^2 N^2} \equiv \sqrt[3]{T^2 MG \over 4\pi^2}
  4. r = {v^2 \over a}
  5. r = {MG \over v^2}
  6. r \equiv \sqrt{MG \over a}

v

  1. v = \omega r \equiv 2\pi N r \equiv {2\pi r \over T}
  2. v = {a \over \omega} \equiv {a \over 2\pi N} \equiv {T a \over 2\pi}
  3. v = \sqrt[3]{\omega MG} \equiv \sqrt[3]{2\pi N MG} \equiv \sqrt[3]{2\pi MG \over T}
  4. v = \sqrt{r a}
  5. v = \sqrt{MG \over r}
  6. v = \sqrt[4]{a MG}

a

  1. a = \omega r^2 \equiv {4\pi^2 r \over T^2} \equiv 4\pi^2N^2 r
  2. a = \omega v \equiv {2\pi T \over v} \equiv 2\pi N v
  3. a = \sqrt[3]{\omega^4 MG} \equiv \sqrt[3]{16\pi^4 MG \over T^4} \equiv \sqrt[3]{16\pi^4N^4 MG}
  4. a = {v^2 \over r}
  5. a \equiv {MG \over r^2}
  6. a = {v^4 \over MG}

Gravitational

MG

  1. MG = \omega^2 r^3 \equiv {4\pi^2 r^3 \over T^2} \equiv 4\pi^2N^2 r
  2. MG = {v^3 \over \omega} \equiv {T v^3 \over 2\pi} \equiv {v^3 \over 2\pi N}
  3. MG = {a^3 \over \omega^4} \equiv {T^4 a^3 \over 16\pi^4} \equiv {a^3 \over 16\pi^4N^4}
  4. MG = rv2
  5. MG = r2a
  6. MG = {v^4 \over a}