A satellite is an object in space that orbits or circles around a larger object. Depending upon which the larger object is different “centric” classifications exists:

- Geocentric orbit: Geo refers to Earth, hence an orbit around Earth
- Heliocentric orbit: Helio refers to Sun, hence an orbit around Sun

Likewise, we have Galactocentric orbit (around galaxy’s centre), selenocentric orbit (around moon) and Areocentric orbit (*any guesses? Hint: planet Elon Musk is most interested in*) and so on.

In our recent post https://www.instagram.com/p/ByGJB_VgRXx/ we have provided a brief description about geocentric orbits (classifications based on altitudes). Today let’s understand the technicalities behind it.

The altitude of the orbit from the Earth’s surface determines how quickly the satellite moves around the Earth. The velocity of the satellite is given by the equation:

v = Sqr_root(GM/R)

The time period of the satellite i.e. the time taken to complete one revolution around the Earth is given by:

T^{2 }= (4*pi*pi*R*R*R)/GM

where, G = 6.673 x 10-11 Nm^{2}/kg^{2}

M is the mass of the Earth

R is the orbital radius (i.e. Radius of Earth + Height of the satellite from Earth’s surface).

Based on the above formulae we can conclude the proportionality of various parameters (directly or inversely). An interesting conclusion is that: satellite mass doesn’t come into picture!

Thus, changing a satellite’s height will also change its orbital speed. This introduces a strange paradox. If a satellite operator wants to increase the satellite’s orbital speed, (s)he can’t simply fire the thrusters to accelerate the satellite. Doing so would boost the orbit (increase the altitude), which would slow the orbital speed. Instead, (s)he must fire the thrusters in a direction opposite to the satellite’s forward motion, an action that on the ground would slow a moving vehicle. This change will push the satellite into a lower orbit, which will increase its forward velocity.

Apart from height, eccentricity and inclination affect’s satellite’s orbit. The eccentricity (e) of an orbit indicates the deviation of the orbit from a perfect circle (Figure 1). A circular orbit has an eccentricity of 0, making a satellite equidistant from earth at all times. Whereas this varies when e is less than 1.

Orbital inclination is the angle between the plane of an orbit and the equator. An orbital inclination of 0° is directly above the equator, 90° crosses right above the pole, and 180° orbits above the equator in the opposite direction of Earth’s spin, refer Figure 2.

Hence the three parameters which determines the satellite’s path and its view of the Earth are: satellite’s height, eccentricity and inclination.

Based on the above knowledge what do you think are the applications of satellites when placed in different orbits (with respect to height, eccentricity and inclination)? Do let us know, our next newsletter is based on that.

References:

https://en.wikipedia.org/wiki/List_of_orbits

https://earthobservatory.nasa.gov/features/OrbitsCatalog