Orbital Mechanics

Orbital mechanics is a offshoot of celestial mechanics, the study of the motions of natural celestial bodies such as the moon and planets.

Ever wondered why spacecraft travel the way they do, here is a brief introduction

The Application of Orbital Mechanics

German astronomer Johannes Kepler (1571–1630) uses the term ‘satellite’ to describe the moons orbiting Jupiter. He develops the three laws of planetary motion, and his accurate astronomical tables provide evidence for the Copernican heliocentric model.

Kepler’s laws

Kepler realised the orbits of the planets could be elliptical rather than circular. Using Brahe’s data on the movement of Mars, Kepler developed his laws of planetary motion.

Kepler's laws

Delta V / Δv

To launch a rocket we need to increase its velocity(V). To move from one orbit to another we need to change its velocity(V)

Orbital Mechanic changes require that either the attraction due to mass or the use of energy to change the velocity(V)

Change in mathematics and physics we use the greek letter Δ(delta) so the change in velocity is called Delta V (Δv)

Note lower case delta(δ) refers to a small change is used (anyone who has studied maths will have used this in calculus as in δx and δy often written dx a small change in x or dy a small change in y)

To get into orbit from a planet (or any massive object) requires a increase of velocity with respect to the planet, this change in velocity is referred to as Delta V / Δv

The same applies to any orbital maneuver it requires a change in velocity Δv, an increase in Δv will increase its orbit or if enough Δv is used to leave the orbit all together called the escape velocity, a decrease in Δv will lower the orbit, enough change will cause a deorbit due to the mass attraction (gravity - all mass attracts other mass), Orbit is achieved when there is enough relative velocity to counter the attraction due to mass (the gravity) also known as freefall of the rocket around the planets mass.

Mass attraction is due to the dilation (perbertations) in the space time topology around it.

Another useful fact is that the effect of mass (Gravitational pull) is reduced by distance squared. At twice the distance (measured from the core of the planet/sun, not the surface) the pull is reduced to a quarter, This is why escape velocity is achievable, as it is possible to go at a speed where the change of the pull reduces faster than the pull itself, which means that it will never slow down to zero.

How do spacecraft navigate in space ?

Laws of Gravity

How does Earth Move around the sun, galaxy and local group

Fun fact: The Earth has rotated around the Milky way approximately 6 times in its existence

Orbital velocity

The orbital speed of a revolving body in a gravitational field.

In gravitationally bound systems, the orbital speed of an astronomical body or object is the speed at which it orbits around either the barycentre or, if one object is much more massive than the other bodies in the system, its speed relative to the centre of mass of the most massive body

v = orbital velocity

a = length of the semimajor axis in meters

T = orbital period