Question E2A06:
What are Keplerian elements?  

Choices:  
A: Parameters that define the orbit of a satellite  
B: Phase reversing elements in a Yagi antenna  
C: High-emission heater filaments used in magnetron tubes  
D: Encrypting codes used for spread spectrum modulation    

Correct Answer is  A: Parameters that define the orbit of a satellite  

Correct answer: A — Parameters that define the orbit of a satellite

1) Why A is correct
- Keplerian elements are a set of parameters that completely specify a satellite’s orbit at a given epoch (time). They define the size, shape, orientation, and current position in the orbit.
- The classical six elements are:
  - $a$: semi-major axis (orbit size)
  - $e$: eccentricity (orbit shape)
  - $i$: inclination (tilt relative to Earth’s equator)
  - $\Omega$: right ascension of the ascending node (RAAN; node longitude)
  - $\omega$: argument of perigee (orientation of ellipse in its plane)
  - $M_0$ (or $\nu_0$): mean anomaly (or true anomaly) at epoch (position along the orbit)
- In practice (TLEs), you’ll see $i$, $\Omega$, $e$, $\omega$, mean anomaly, and mean motion, plus epoch and drag terms.

2) Why the other choices are incorrect
- B: Phase-reversing elements in a Yagi antenna are phasing/parasitic elements, not “Keplerian.” Keplerian relates to orbital mechanics, not antennas.
- C: Magnetron heater filaments are tube components; nothing to do with orbital parameters.
- D: Spread spectrum uses pseudorandom codes (e.g., PN sequences), not Keplerian elements.

3) Useful formulas and rules of thumb
- Orbital period (using Earth’s gravitational parameter $\mu \approx 3.986\times10^{14}\ \text{m}^3/\text{s}^2$):
  $$T = 2\pi\sqrt{\frac{a^3}{\mu}}$$
- Mean motion:
  $$n = \sqrt{\frac{\mu}{a^3}} = \frac{2\pi}{T}$$
  In TLEs, mean motion is often given in revolutions per day; then:
  $$T\ (\text{seconds}) = \frac{86400}{n_{\text{rev/day}}}$$
- Perigee and apogee distances from Earth’s center:
  $$r_p = a(1 - e), \quad r_a = a(1 + e)$$
  Altitude = distance − Earth radius (approximately $6378\ \text{km}$).
- Rule of thumb: LEO satellites (common for ham sats) have $T \approx 90$–100 minutes, mean motion $\approx 14$–16 rev/day.