Orbit

Orbital Facts of Planets:

1. Planets orbit the sun in a counter-clockwise direction.
2. Most planets besides Mercury and Pluto orbit in a confined plane, usually with +3 or –3 degrees that of the Earth’s orbital plane. Mercury’s orbital plane, is 7 degrees variation of Earth’s while Pluto’s is 17 degrees variation of Earth’s.
3. Most planets’ orbits are circular except Mercury’s and Pluto’s which is oval.
4. The spin axes of most planets and moons are perpendicular to their orbital plane. This is with the exception Venus and Uranus in our Solar System, because it has been interfered by some other forces, probably from a collision or additional or too little gravity affecting it.

The Spin axe is the axis of which the planet is spinning.

This relates the planets and stars, mostly with this property, as gyroscopes.

Angular momentum

Objects having a constant motion around its own axis possess a physical quantity called angular momentum. Numerous experiments have all proved that angular momentum cannot be destroyed. As a result, the conservation of angular momentum demands that the angular momentum quantity must always be constant in a closed system and only its constituents’ quantity may vary.

Angular momentum can be found in cases like planets orbiting their star, as well as in a top.

Spin direction

L= I

L=Angular momentum

I=moment of inertia

=Angular velocity

L=mvr

L=Angular momentum

m=mass of planet A

v=velocity of orbit

r=distance of separation between the two objects

Orbiting planet and orbited object in the middle considered as a whole system (including the space between the sun and the planet) spinning on its own axis (the sun).

In both cases of angular momentum calculation, both are mathematically reasonable in the conservation of angular momentum when there is a change in quantity in each variable.

In astronomy, we would be looking more at the example of the orbiting planet. The conservation can be explained as below.

The above formula can be rearranged to give v = L/(mr).

Since angular momentum L is a constant for an isolated system, the velocity v and the separation r are inversely correlated. Thus, conservation of angular momentum demands that a decrease in the separation r be accompanied by an increase in the velocity v, and vice versa.

Decrease in separation=increase in velocity

Elongation: The angular distance between two celestial bodies as seen from Earth. \

Retrograde motion : The orbital motion of a body in a direction opposite that which is normal to spatial bodies within a given system. In this case, the exception is referred to as a clockwise direction.

Prograde motion: The orbital motion which is in the direction normal to most spatial bodies within a given system. In our solar system, the prograde refers to an anti-clockwise direction.

Most moons of planets and most planets in our solar system have a Prograde orbit.

Venus, Uranus, Ananke, Carme, Pasiphaë and Sinope of Jupiter, Phoebe of Saturn and Triton of Neptune all have retrograde motions.

The direction of Prograde motions is that of the spinning accretion disk during the formation of the solar system, which is anti-clockwise. Thus, the forming protoplanets and protosun too possess a spin direction of the accretion containing them.

Retrograde motion is caused by external influences which affect the direction of the planets’, sun’s or moons’ spin. They include a collision with another astronomical body, or an asteroid moving in the clockwise direction and being captured by the gravity of a nearby planet, forming a moon with a retrograde motion.

Retrogradation: The phenomenon observed in the planets further than the Earth, Mars and onwards. When the earth rotates on its usual west to east Prograde motion, the planets, for example Mars, appear to move from east to west across the sky but be drifting eastward with respect to its background as observed on Earth. However, when the Earth completes its orbit faster than the Mars, and overtakes it, the planet would seem to be drifting westwards instead, as it is lagging behind us. This is usually observed for planets further from the sun than the Earth.

### Elliptical Orbits

Many people have the misconception of planets rotating in circles, but they are wrong, planets rotate in ellipses.

1. For an ellipse, there are two fixed points called foci, singular: focus. An ellipse is a near-circular shape, but for any point on the ellipse, the sum of both distances to the foci from that point must always be a constant.

a + b=constant

2. The side-to-side variation in shape of an ellipse is called the eccentricity. The greater the widening or narrowing of the ellipse from left to right, the higher the eccentricity. Mercury and Pluto have highly eccentrical orbits. A circle may be viewed as a rare case of an ellipse with zero eccentricity. As the side-to-side variation increases, the eccentricity approaches one. Most ellipses have eccentricities lying between zero and one.

Most planets have small eccentricities in their orbits such that they look circular. Mercury and Pluto are exceptions in our solar system with high orbital eccentricities such that they look oval.

3. The horizontal and longer axis of the ellipse is the major axis, while the vertical and shorter axis is the minor axis. Half of the major axis is termed a semi-major axis.

The length of a semi-major axis is often named as the size of the ellipse. It can be shown that the average separation of a planet from the Sun as it goes around its elliptical orbit is equal to the length of the semi-major axis. As a result, the radius of the planet’s elliptical orbit around the sun can also be termed as the semi-major axis of the ellipse.

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