An electron jumps from orbit of higher energy to an orbit of lower energy which radiates energy in form of photons. The energy emitted is equal to difference in the energies from the two orbits.

The equation or formula for Bohr model for third postulate is given as,

hv = E_n – E_p

ΔE= E_n – E_p

ΔE = difference in energies of higher orbit and lower orbit.

E_n = energies of nth higher orbit and E_p =energies of p^th lower orbit

h = Planck’s constant

v = frequency of radiation emitted or absorbed

Electron of an atom orbiting around a nucleus are permitted to revolve in those orbit for which angular momentum is equal to integral multiple of h/2π, where h is the Planck’s constant.

The equation or formula for Bohr model for postulate 2 is given as,

m v_n r_n = n h / 2π

m= mass of an electron (9.1 x 10–31 Kg)

v_n = velocity of electron in nth state (orbit)

h= Planck’s constant (6.67 x 10^–34 J-s)

r_n = radius of nth orbit

n is a positive integer

The electron in an atom is restricted to revolve in certain allowed circular orbit known as stationary orbit. The centripetal force for its motion is provided by electrostatic force of attraction between positively charged nucleus and negatively charged electron.

The equation or formula for Bohr model for first postulate is given as,

mv² / r_n = KZe² / r_n²

m= mass of an electron (9.1 x 10–31 Kg)

v = Frequency of radiation which is either emitted or absorbed.

r_n = radius of nth orbit

Z= atomic number (No. of Protons)

e = charge of electron.

K = 1/(4πε₀) = coulomb’s constant = 9 x 10⁹ N m² C^–2

In orbital mechanics, Kepler’s equation relates various geometric properties of the orbit of a body subject to a central force.
The formula Kepler’s equation for calculating orbits is given as,

M = E – ϵ sin E

M = the mean anomaly
E = the eccentric anomaly
ϵ = the eccentricity

It is a transcendental equation because sine is a transcendental function. It means that it cannot be solved for E algebraically. Numerical analysis and series expansions are generally required to evaluate E.

A body traveling along hyperbolic trajectory will attain in infinity an orbital velocity called hyperbolic excess velocity (v_∞).

The formula for Hyperbolic excess velocity is given as,

v_∞ = √〈µ / -a〉

v_∞  = Hyperbolic excess velocity

µ  = is the standard gravitational parameter

a = the length of the semi-major axis (a > 0 for ellipses, a = ∞ or 1/a = 0 for parabolas,

                                                                   and a < 0 for hyperbolas)