Eccentricity is a number from 0 to just under 1 that tells how stretched an orbit is: 0 is a perfect circle, and values near 1 are long, thin ellipses.
Every closed orbit is an ellipse, and a circle is just an ellipse that is not stretched at all. Eccentricity measures the stretch.
An ellipse has two special points inside it called foci; the planet sits at one of them. NASA defines eccentricity as the distance between the foci divided by the long axis of the ellipse. If the foci sit on top of each other, the eccentricity is 0 and the orbit is a circle.
Indian satellites span almost the whole range:
For comparison, a Molniya orbit has e = 0.722, and Halley's Comet has 0.967. Even the Moon's orbit around Earth is slightly stretched: from about 363,300 km to about 405,500 km, which works out to e ≈ 0.055.
Some jobs need near-perfect circles. A geostationary satellite must have an eccentricity of zero to stay over one point. Even retired satellites are held to this: the graveyard orbit above GEO is meant to be nearly circular, with an eccentricity of 0.003 or less. ISRO quoted that limit when it retired GSAT-12 in 2023.
Many low-orbit imaging satellites are also close to circular. Cartosat-3's catalogue orbit varies by only 16 km, from 500 to 516 km, so the ground below is always seen from nearly the same distance.
If a spacecraft goes fast enough, its path stops closing on itself. An eccentricity of exactly 1 is a parabola and above 1 is a hyperbola; either way, the spacecraft escapes. Mangalyaan did this on 1 December 2013, when its trans-Mars injection burn broke it free of Earth's orbit.
NVS-02's orbit has an eccentricity of about 0.74: on the globe its path is a long loop, not a ring. Track NVS-02
With r_p and r_a measured from Earth's centre:
e = (r_a − r_p)/(r_a + r_p), a = (r_a + r_p)/2, r_p = a(1 − e), r_a = a(1 + e).
Worked numbers (R = 6,378 km):
Two results make eccentricity easy to reason about. First, the orbit's energy per kilogram depends only on a: ε = −GM / (2a). Second, so does the period: T = 2π√(a³/GM). Stretching an orbit while keeping a fixed changes its shape but not its period. NVS-02's 660-minute period is exactly what a circular orbit of radius 25,111 km would have.
The conic-section table follows from the energy. Negative energy (a > 0) gives e < 1 and a closed ellipse. Zero energy gives e = 1, a parabola, the exact escape case. Positive energy gives e > 1, a hyperbola. Escape speed is therefore √2 times the circular speed at the same radius: at 288 km altitude, 10.94 km/s versus 7.73 km/s.
Zero. The two foci coincide at the centre, so there is no stretch.
e = (43,629 − 6,592)/(43,629 + 6,592) = 37,037/50,221 ≈ 0.74.
The path no longer closes; it becomes a parabola (e = 1) or hyperbola (e > 1) and the spacecraft escapes the planet.