Orbital MechanicsOrbit, acceleration and escape speed

Chapter 2 :

Ellipse and Hyperbole are not just figures of speech.

Johannes Kepler1571 - 1630

Orbital MechanicsOrbit, acceleration and escape speed

Can we reach orbit or get to the Moon with a cannon ?

Orbital MechanicsOrbit, acceleration and escape speed

Newton's Cannon

Can we reach orbit or get to the Moon with a cannon ?

Orbital MechanicsOrbit, acceleration and escape speed

Yes, if the horizontal velocity is sufficient. The faster we are, the farther we'll go, until we'll "miss" the Earth, then we'll be in orbit.

Can we reach orbit or get to the Moon with a cannon ?

Orbital MechanicsOrbit, acceleration and escape speed

What defines an orbit ?

Orbital MechanicsOrbit, acceleration and escape speed

What defines an orbit ?

Orbital MechanicsOrbit, acceleration and escape speed

An velocity (with orientation) and a center of mass define an orbit. The altitude doesn't really matter. It's all about speed. The mass of the object doesn't matter for its own orbit. Therefore, we can predict the trajectory of a planet simply by knowing the mass of the

Sun and the velocity of the planet Apoapsis : the farthest point from the celestial body which an object orbits around Periapsis : the nearest point from the celestial body which an object orbits around

What defines an orbit ?

Orbital MechanicsOrbit, acceleration and escape speed

How to orient ourselves on an orbit ?

Orbital MechanicsOrbit, acceleration and escape speed

How to orient ourselves on an orbit ?

Orbital MechanicsOrbit, acceleration and escape speed

Prograde : in the direction of movement. Retrograde : in the opposite direction of movement Radial in: 90° towards the center of gravity Radial out : 90° outwards from the center of gravity Normal: 90° "north / up" Anti-normal : 90° "South / down"

Acceleration Prograde : increases the velocity, elongation of the orbit. Retrograde : reduces the velocity, contraction of the orbit. Radial in or out : rotates the ellipse's axis Normal or anti-normal : changes inclination of the orbit's plane

How to orient ourselves on an orbit ?

Orbital MechanicsOrbit, acceleration and escape speed

What is the consequence of an acceleration without changing orientation ?

Orbital MechanicsOrbit, acceleration and escape speed

What is the consequence of an acceleration without changing orientation ?

Orbital MechanicsOrbit, acceleration and escape speed

We get ourselves on an elliptical orbit, but this doesn't affect where we are, just the path we'll follow.

If we accelerate too much, we switch to an hyperbolic trajectory, we won't return around the central planetary body.

Higher the orbit is, lower is the average speed, even though we had to increase speed to get there.

→ In orbital mechanics, the more we accelerates, the lower the average speed will be !

What is the consequence of an acceleration without changing orientation ?

Orbital MechanicsOrbit, acceleration and escape speed

Where is the best location to accelerate ?

Orbital MechanicsOrbit, acceleration and escape speed

Where is the best location to accelerate ?

Orbital MechanicsOrbit, acceleration and escape speed

Direction change (normal or radial) :→ The farther from the center of mass we can, where linear speed is the lowest (because we have to change the orientation of the velocity)

Linear velocity change (prograde or retrograde)→ At the nearest location (periapsis) from the center of mass (Oberth's effect), where the linear speed is the highest.

In some cases, the location of the burn can't be chosen freely.

Where is the best location to accelerate ?