Circular Motion

Requires the motion of gravitational attraction and centripetal forces
F(centripetal) = F(gravity)
mv^2/r = GMm/r^2
v^2 GM/r

We also need the critical infor
mation of Kepler's Third Law
R^3/T^2 = GM/4π^2

Low Earth Orbit Satellites usually has a period of 90 minutes
if calculated they travel at 8km/sec

The period for Geostationary Orbit, are the same as an Earth day; 24 hours
The radius for GEO sats. would be roughly 42 000 km.
GEO Satellites are very usually as they will appear motionlessly in the sky and are not subjected to atomspheric drag.

Kepler's Law of Planetary Motion

In astronomy, Kepler's laws of planetary motion are three scientific laws describing the motion of planets around the Sun.

Kelper's 1st Law

Kepler's 1st Law (Law of Orbit) involves Stellar Parallax where the motion of Earth causes (when obversing a star) to move forth and back in the background. It states that two objects interact gravitationally, they will experience an conic shape (cross section of a cone on an angle)

If the interaction are permanent (gravitationally bounded orbits), then they will experience an elliptic shape or an encase cyclinderical cross section. An example of this is the Moon orbitting around Earth, or the Earth orbitting the Sun

If the interaction are not permanent (open orbits), then they will undergoes an parabolic or hyperbolic shape. This concept of open orbit can be found with the slingshot effect.

KEYWORDS TO NOTE : Ellipticity, eccentric, major axis, semi major axis

Kelper's 2nd Law

Kepler's 2nd Law (Law of Area) states that two objects whether in a closed orbit or not, will have equal areas when joining the lines in the equal time interval
It provides that an object in elliptic orbits are not subjected to a constant velocity, rather when the object is closer, its travels faster compared
to an object that orbits further from the central object.

An Apogee is point in the orbit of the moon or a satellite at which it is furthest from the earth.

A Perigee is point in the orbit of the moon or a satellite at which it is closest

Kelper's 3rd Law

Kepler's 3rd Law (Law of Period)states that the total mass of the two focal objects time square of the period is proportional to the cube of the size of the orbit, which
for an elliptical orbit is the semi-major axis of the ellipse.

R^3/T^2 = GM/4π^2

Retrograde Motion

When an objects moving is motion within a object that it is orbiting, it is known as an epicycle.
However, epicycles are used in Geocentric, stating the Earth was at the centre of the Solar System.
Where as, Heliocentric, suggested the Sun was as the centre of the Solar System.

Both able to undergoes retrograde motion, as such where a the planet at start moves in a straight motion, but turn around in a forming a slim oval before moving in the exact same straight motion.

Energy of Orbit

KE

Kinetic Energy

The energy of an object, also known as Kinetic energy is given by 1/2(m)(v^2) and as the is subjected to gravity, its velocity is v^2 = GM/r Hence:

KE = GMm/2R

GPE

Gravitational Potential Energy

Since an objected will always to subjected to a planet's gravity, no matter the there radius, they will experience GPE Hence scientist take the reference point of max distance, ∞ Hence:

GPE = - GMm /r

Escape Velocity

Newton's Mountaintop Cannon

A cannonball is placed a the top of high mountain. It is shot at different velocity Earth.

Slow Velocity : The ball is be subjected by gravity and fall to the ground.
Faster Velocity : The ball will have the same effect, except fall further away.
Orbital Velocity : The ball will continue to fall infinitly due to the curvature of

Escape Velocity

The minimum velocity required to propel a rocket towards infinity
and not fall back under the influence of gravitation attraction.
Hence,
GPE + KE = 0
v(escape) = (GM/R^2)^1/2

IMPORRANT NOTE that in reality, a projectile object, isn't throw wih respect the the horizontal, as Earth is round, but since for simplicity and the insignificant, we treat it as flat.

Changing Orital Altitude

There are two types of methods to change the orbital altitude,

Posigrade: Increases velocity, whilst increase size of orbit
Retrograde: Decreases velocity, whilst decrease size of orbit

Another methods, this for transfering orbits from one planet to another is through Hohmann Transfer Orbit where in order to jump to another orbit
of a planet, they must undergoes another burn.

Changing Orbital Inclination

To change an orbital incline is changing its angle each which its makes with the Equator.
To achieve this, the satellite, must be subjected to an 90 degree (perpendicular angle) to the satellite, to create that upwards motion, to increase its inclination of the satellite orbit.

Interplanetary Orbit

Interplanetary Orbits is dealt with Gravity Asssist or the Slingshot Effect. Refer to Information on HSC Physic.

Orbital Rendezvous

This section tries to explains the how rockets or supply spacecrafts, are used to meet with the satellites in orbit. It's not as simple as launching it up to the point, and hence astronuats must consider the Rendezvous Points to help acheive a safe and successful contact of shuttle and satellites in orbit.

The most important aspect is the Timeliness as the supply shuttle must be launched at the right time to the right orbits, to reach its destination. Another factor is an intermediate Orbit the space craft must orbit. It should be placed lower than the destination's orbits, as a lower obrit provides a faster velocity to catch up with the destinated satellite's orbits.

Once you reach their orbits, there are three possible outcomes, the spacecraft is infront, reachable, or behind.

Infront: Since the spacecraft is infront, it must move quicker for the orbital satellite to catch up and be reached. Hence the spacecraft should undergo a posigrade to increase velocity and increase its obital altitude. This in turns of increasing altitude, make the satellite orbits faster and overtake the spacecraft.
Behind: Since the spacecraft is behind, it must slow down for the orbital satellite to catch up and be reached. Hence the spacecraft should undergo a retrograde to decrease velocity and decrease its obital altitude. This in turns of decreasing altitude, make the satellite orbits slower so the spacecraft can catch up.