Orbital perturbation

The deviation of the satellite from the predetermined path due to external disturbances is known as orbital perturbation.

The main causes of orbital perturbation are:

I. Effect of sun and moon

II. Effect of non-spherical earth

III. Atmospheric drag

IV. Solar radiation pressure

I. Effect of sun and moon

• Gravitational attraction by sun and moon causes orbital inclination of geostationary satellite to change with time if not countered by north-south station keeping, these forces would increase the orbital inclination from an initial zero degree at launch to14.67°, 26.6 years later.
• The moon and the sun both create a gravitational potential on the satellite which causes it to perturb.

II. Effect of non-spherical earth

It is known to us that earth is not perfectly spherical, their being an equatorial bulge and flattening at the poles it is called as oblate spheroid. This oblate shape of earth causes perturbation of satellite.

a.Change in orbital period

• For a spherical earth of uniform mass kepler’s third law gives the nominal mean motion n_0 as :

n0=2πTrad/sec$n_0=\frac{2\pi /}{T}rad/sec$

• The subscript ‘0’ is included as a reminder that this result applies for a perfectly spherical earth of uniform mass. However earth is described as oblate spheroid so its mean motion is given by:

n=n0[1+k1(1−1.5sin2i)a2(1−e2)1.5]$n=n_0[\frac{1+k_1(1-1.5si{n}^{2}i)}{a^2(1-e^2{)}^1.5}]$

where,k1isconstant$where,k_{1}isconstant$

aissemimajoraxis$aissemimajoraxis$

eiseccentricity$eiseccentricity$

• This orbital period taking into account Earth’s oblateness is called anomalistic period:

T=2πnsec$T=\frac{2\pi /}{n}sec$

b. Regression of nodes

• Regression of nodes is a rotation of the orbital plane in the direction opposite to the satellite motion around the axis of rotation of the earth.
• Due to regression of nodes, the nodes (ascending and descending nodes) appear to slide across the equator.
• If orbit is prograde, the nodes slide westward and if retro grade they slide eastward.
• It causes Ω$\Omega$ the right ascension of the ascending node shifts its position

dΩdt=−kcosi$\frac{d\Omega /}{dt}=-kcosi$

Where,i–inclinationangle$Where,i–inclinationangle$

• For Polar orbits regression of nodes is zero (∵i=90°)$(\because i=90°)$.

c.Rotation of line of Apsides

• The rotation of line of Apsides is the rotation of ellipse major axis around the center of the earth on a fixed orbital plane.
• Due to rotation of line of Apsides ω the argument of perigee changes with time

dωdt=k(2−2.5sin2i)$\frac{d\omega /}{dt}=k(2-2.5si{n}^{2}i)$

• At i=63.43°$i=63.43°$, no rotation takes place since the term 2−2.5sin2i=0$2-2.5si{n}^{2}i=0$

d. Drift due to Equatorial ellipticity

• The earth is not perfectly circular in the equatorial plane; it has small eccentricity of order〖 10〗^(-5).
• This leads to gravity gradient which causes the satellite in the geostationary orbit to drift to one of the two stable points called as satellite graveyards.
• These points are at 75°E$75°E$ and 105°W$105°W$. Satellites in service are prevented from drifting to these points by station keeping.

III. Atmospheric drag

• For near satellite below about 1000km, the effects of atmospheric drag are significant because the drag is greatest at the perigee.
• The drag acts to reduce the velocity at the perigee point, with the result that the does not reach the same apogee height on successive revolution.
• As a result both eccentricity (e) and semimajor axis (a) are reduced.

IV. Solar radiation pressure

• Solar radiation pressure from sun rays perturbs the satellite orbit.
• The satellite experiences change in eccentricity. It builds up for 1st sixth months and then shrinks for the next sixth months.

Look Angles and Orbit perturbation

Earth station will receive the maximum signal level, if it is located directly under the satellite. Otherwise, it won’t receive maximum signal level and that signal level decreases as the difference between the latitude and longitude of earth station increases.

So, based on the requirement we can place the satellite in a particular orbit. Now, let us discuss about the look angles.

Look Angles

The following two angles of earth station antenna combined together are called as look angles.

• Azimuth Angle
• Elevation Angle

Generally, the values of these angles change for non-geostationary orbits. Whereas, the values of these angles don’t change for geostationary orbits. Because, the satellites present in geostationary orbits appear stationary with respect to earth.

These two angles are helpful in order to point at the satellite directly from the earth station antenna. So, the maximum gain of the earth station antenna can be directed at satellite.

We can calculate the look angles of geostationary orbit by using longitude & latitude of earth station and position of satellite orbit.

Azimuth Angle

The angle between local horizontal plane and the plane passing through earth station, satellite and center of earth is called as azimuth angle.

The formula for Azimuth angle (α$\alpha$) is

α=1800+Tan−1(TanGTanL)$$\alpha ={180}^0+Ta{n}^{-1}\left(\frac{TanG}{TanL}\right)$$

Where,

• L is Latitude of earth station antenna.
• G is the difference between position of satellite orbit and earth station antenna.

The following figure illustrates the azimuth angle.

Measure the horizontal angle at earth station antenna to north pole as shown in figure. It represents azimuth angle. It is used to track the satellite horizontally.

Elevation Angle

The angle between vertical plane and line pointing to satellite is known as Elevation angle. Vertical plane is nothing but the plane, which is perpendicular to horizontal plane.

The formula for Elevation angle (β$\beta$) is

β=Tan−1(cosG.cosL−0.151−cos2G.cos2L−−−−−−−−−−−−−√)$$\beta =Ta{n}^{-1}\left(\frac{cosG.cosL-0.15}{\sqrt{1-co{s}^{2}G.co{s}^{2}L}}\right)$$

We can calculate the elevation angle by using above formula. The following figure illustrates the elevation angle.

Measure the vertical angle at earth station antenna from ground to satellite as shown in the figure. It represents elevation angle.

Orbital Perturbations

Following are the orbital perturbations due to gravitational and non-gravitational forces or parameters.

• Irregular gravitational force around the Earth due to non-uniform mass distribution. Earth’s magnetic field too causes orbital perturbations.
• Main external perturbations come from Sun and Moon. When a satellite is near to these external bodies, it receives a stronger gravitational pull.
• Low-orbit satellites get affected due to friction caused by collision with atoms and ions.
• Solar radiation pressure affects large GEO satellites, which use large solar arrays.
• Self-generated torques and pressures caused by RF radiation from the antenna.

Most satellites use a propulsion subsystem in order to maintain a proper spin axis direction and control the altitude of the satellite against perturbation forces.

Daily updates 3-July-2019

International News

1. USA designates Baloch Liberation Army as terror group
i. The Department of State of USA has designated the Balochistan Liberation Army (BLA) and Hizballah operative Husain Ali Hazzima as Specially Designated Global Terrorists.
ii. The USA has also blamed the organizations for the attacks on Chinese assets amid an ongoing civil war like situation in Pakistan’s biggest province Balochistan.

2. U.S. Senate passes provision to give India NATO ally-like status
i. The U.S. Senate has passed a legislative provision National Defense Authorisation Act  for India. 
ii. The act will bring India at par with America’s NATO allies which will increase U.S.-India defence cooperation in the Indian Ocean in the areas of humanitarian assistance, counter terrorism, counter-piracy and maritime security. 
iii. The act has been passed for the fiscal year 2020.
Static/Current Takeaways Important For SBI PO/Clerk Mains:

President of USA: Donald Trump; Capital: Washington, D.C

Banking and Business News

3. RBI fines 4 Public Sector Banks for violating KYC norms
i. The Reserve Bank of India has imposed penalties on four state-run lenders for violating Know Your Customer norms and anti-money laundering standards.
ii. Punjab National Bank, Allahabad Bank, and UCO Bank were fined Rs 50 lakh each while Corporation Bank was fined Rs 25 lakh.
Static/Current Takeaways Important For ESIC:

RBI 25th Governor: Shaktikant Das, Headquarters: Mumbai, Founded: 1 April 1935, Kolkata.

4. Ola Electric gets $250m funding from SoftBank
i. Japanese company SoftBank has invested around $250 million in Ola Electric Mobility. 
ii. With this investment, Ola Electric has become the newest unicorn of India, joining the list of companies like Flipkart, Zomato and Paytm.
Static/Current Takeaways Important For EPFO/LIC ADO Mains:

CEO of Ola Electric: Bhavish Aggarwal.

CEO of Softbank Corp.: Ken Miyauchi, Chairman: Masayoshi Son.

State News

5. Campaign to eradicate AES and JES launched in UP
i. Chief Minister of Uttar Pradesh have launched the IInd phase of Communicable Disease Control and Dastak Abhiyan 2019. 
ii. The campaign is launched to eradicate deadly Acute Encephalitis Syndrome and Japanese Encephalitis disease.
iii. The state wide program was organized under the banner of Health department and UNICEF. iv. Chief Minister flagged off the vehicles of awareness campaign and also honored the Dastak Yoddhas by awarding certificates.
Static/Current Takeaways Important For EPFO/LIC ADO Mains:

Chief Minister of Uttar Pradesh: Yogi Adityanath; Governor: Ram Naik.

Defence 

6. Indo-French Joint Air Exercise Garuda-VI Begins
i. The Indian and French Air Force has started Garuda VI exercise at Mont de Marsan in France.
ii. The exercise is scheduled to take place from 1 July to July 12, 2019, in France.
iii. The Indian Air Force (IAF) contingent comprises of 120 air-warriors and four Sukhoi 30 MKI along with an IL-78 flight refuelling aircraft.
Static/Current Takeaways Important For RRB NTPC/IBPS RRB Mains:

Air Chief Marshal BS Dhanoa is the present Chief of the Air Staff of IAF.

Appointments

7. N S Vishwanathan gets extension by one year as RBI deputy governor
i. Reserve Bank of India Deputy Governor N S Vishwanathan has been given a one-year extension by the GoI. Presently he is heading the Department of Banking Regulation of the Reserve Bank of India.
Static/Current Takeaways Important For RRB NTPC/IBPS RRB Mains:

RBI 25th Governor: Shaktikant Das, Headquarters: Mumbai, Founded: 1 April 1935, Kolkata.

8. Manoj Kumar Nambiar elected chairman of MFIN
i. Microfinance Institutions Network has elected Manoj Kumar Nambiar as its chairman. 
ii. MFIN comprises 56 NBFC-MFIs and 40 associates including banks, small finance banks and NBFCs.
Static/Current Takeaways Important For ESIC:

Chief Executive Officer of MFIN: Harsh Shrivastava; Founded: December,2009.

Sports News  

9. Ambati Rayudu retires from international cricket
i. Indian batsman Ambati Rayudu has announced his retirement from international cricket. 
ii. He has played 55 ODIs for India, scoring 1694 runs at an average of 47.05 with three hundreds and 10 half-centuries.
10. India loses to Pakistan in the IBSF Snooker World Cup finals
i. The Indian team lost to Pakistan in the final of the IBSF Snooker World Cup in Doha. India lost the summit clash by 1-3. 
ii.  Pankaj Advani and Laxman Rawat represented the Indian team in the world cup.