Rocket Science — Basics — Part 3 — Orbits
In this blog post, we will delve into fascinating orbits.
So, Let’s start with what is an Orbit? — It is the trajectory of an object that keeps falling towards something due to gravity but misses out completely due to the high horizontal velocity.
Just to refresh something about ballistic motion. In the image below, we can see that once the missile is fired from the tank, it is fully in the control of gravity. In the horizontal axis, the velocity would remain the same but the vertical axis will be controlled by the gravity. Usually, the trajectory will be a parabola.
You can see that, depending upon the force at which the missile is fired, it determines the horizontal distance that the missile travels and subsequently falls because of gravity which pulls the missile down. Here, we need to understand that the horizontal velocity remains constant.
Now we can think of like the missile is fired in such a way that the horizontal velocity is high and the gravity of the earth is always pulling the missile down but since the earth is spherical, it starts to rotate around the earth.
You can ask me a question, how fast the missile needs to be fired in such a way that it needs to move around the orbit? The answer is 7.6 km/sec for a low earth orbit approximately 200 km above the earth’s surface. There are various levels of orbit which we will see it in depth in the subsequent sections.
You can see in the above animated image, if a person fires a bullet from the surface of earth into orbit and if the velocity of the bullet is very high and the earth’s gravitational pull is high, the object will be in motion (circular) and will never come back to earth. the bullet will revolve around the surface of earth and end up hitting the person itself.
One more fact that many people say wrong is ‘You are in space and it has zero gravity and that’s why astronauts are floating’. This is wrong because of the orbit’s nature, the astronauts are always falling towards the earth, we can say as astronauts are always in free-fall that is the reason why they float in space.
Kepler’s First law of orbits —
Orbits are never circular, they are elliptical.
We know that earth moves around the sun. These laws from Kepler describes how the planets are moving around the sun. According to this law, since the earth moves around the sun in an elliptical orbit, it has two foci or focal points with one major and one minor axis. Sun is at one foci and empty at other foci. The closest point of earth to sun is called as Perihelion and farthest point of earth to sun is called as Aphelion.
In the above picture, we can see that an ellipse contains two focal points that are present in equal distance from the center in opposite direction. In our case, the sun will be present in one foci and empty at the other foci. We can also see that there are two axis, one major axis (horizontal) and other minor axis (vertical).
From the above picture, we can say that the left side of the major axis is called as Perihelion and right side is called as Aphelion. The Perihelion is about 147 million kilometers and Aphelion is about 152 million kilometers.
Kepler’s Second law (law of equal areas) — The radius vector drawn from the Sun to a planet sweeps out equal areas in equal intervals of time.
In the above figure, we can see that if you draw a line from sun to the earth, the area covered by the line in a certain time interval will be same across the elliptical orbit. We can see that the area covered while the planet is in perihelion on the right hand side is equal to the area covered by the planet in aphelion in left side. This shows that the energy near the perihelion is much greater than aphelion. The area swept in equal intervals of time is a constant.
Kepler’s Third Law (The Law of Periods) — The square of the time period of revolution of a planet around the sun in an elliptical orbit is directly proportional to the cube of its semi-major axis.
The equation for this law is T² / R³ = k, where T is the orbital time period (time taken by the planet to complete one revolution), R is the semi-major axis distance and k is a constant. So, we can say that if the planets distance from the sun increases, the time taken for the planet to complete one rotation around the sun will be high. Just for a fact: Earth takes 365 days approx., and Mars takes 687 days approx., to complete one rotation around the sun.
The above depict the three laws of orbits by Kepler.
- First Law — We can see that planet 1 and planet 2 revolve around the sun in an elliptical orbit.
- Second law — The area A1 covered by the planet 1 is same as the area A2 covered by the planet 1 in the same duration. It suggests that planets revolve faster around the perigee and slower in apogee.
- Third law — The time taken by the planet to complete one revolution is directly proportional to the semi major axis of the elliptical orbit. It can be seen from the figure like, the time taken by planet 1 is much lower than planet 2 to complete one revolution.
Types of Orbits:
The orbits can be classified into three categories based on the altitude from the earth. These are:
Low Earth Orbit (LEO) — (~2,000 km and below): We can use this orbit for ISS (International Space Station) and Hubble space telescope. Satellites in LEO have shorter orbital periods, typically around 90 to 120 minutes per orbit. In LEO, the atmospheric drag will be present in a minimum amount. For e.g., ISS has a boosting rocket connected to it in order to mitigate the atmospheric drag by placing the ISS on LEO every 3 to 4 months and Hubble telescope once in every decade since it is placed bit above the ISS. For the fact, ISS is placed at 400 km above the earth surface and the famous Hubble telescope at 550 km.
Now, you must have a question like there are so much satellites in LEO, won’t they collide with each other?
The answer is NO. That is because of two things 1. Orbital Inclination — From the above figure, we can see that the orbits may exactly at the horizontal axis of earth (equator) which we usually call it as reference orbit or it can be 45⁰ degrees or any degree from the reference orbit. This is called as Orbital Inclination. The orbits can be of any different angles but their center must pass through the earth’s center. Now, You would had a another question, Will they not collide at intersection points? The answer is NO. It is because 2. Orbital Phase, i.e., the satellites pass through intersection at different orbital speeds. Also, within a single orbit and within a single inclination, there can be multiple satellites with different phase.
Medium Earth Orbit (MEO) — (Above 2000 km and below 30,000 km): We can use this orbit for GPS navigation. MEO satellites have longer orbital periods, generally around 12 hours. GPS satellites are placed in MEO because of two reasons. 1. We essentially need lesser number of satellites since these are placed at nearly 20,000 km from the earth surface. Anywhere in the world, you will be able to get signals of as much as 7 to 8 GPS satellites. For the fact GPS comes under the umbrella of GNSS (Global Navigation Satellite System). GPS is Navigation satellites by USA, others include Galileo, Baidu etc., 2. There is a phenomenon called as Van Allen Belt.
Van Allen Belts— These are zones of energetic charged particles trapped by Earth’s magnetic field. They consist mainly of electrons and protons that originate from solar wind and cosmic rays. The magnetic field acts like a shield, trapping these particles and preventing them from reaching Earth’s surface, which helps protect our atmosphere from erosion by solar winds. These trapped particles can harm the space systems and satellites.
Geosynchronous Earth Orbit (GEO) — (35,800 km): We can use this orbit for weather and communication. It’s rotation period is same as that of earth because it is fixed over a particular point on Earth surface. The dish TV’ s that we have all works with the satellites in GEO. A few satellites in geostationary orbits can cover large portions of the Earth’s surface since it is kept at a farther distance. For instance, three satellites can provide nearly complete global coverage.
Now, a question, ‘How many satellites we can fit in GEO?’.
The answer is Slots are allocated by the ITU (International Telecommunication Union), so that the satellites avoiding being very close to each other. Also, for the fact that the GEO is packed with satellites from different providers and since it is far from earth, when a satellite reaches culmination, they are pushed a bit outside the GEO so that other satellites can occupy it.
In next post, we will dive deep into other orbital mechanics and some interesting topics. Stay Tuned !!!
Thanks for reading !!!
