Foundations — Orbit types — LEO, MEO, GEO, HEO, SSO, Molniya

Before you can read the parent note Orbit types, you must own every symbol it throws at you. This page builds each one from nothing — plain words, then a picture, then why the topic can't live without it. Read top to bottom; each block uses only symbols defined above it. Each figure is called out by number in the text — look for "Figure 1", "Figure 2", and so on.

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1. The circle and its pieces — $r$, $R_{\oplus }$, $h$

Picture a satellite as a dot going around a big ball (Earth). Three lengths describe "how high up" it is. See Figure 1.

Figure 1 — the three lengths $R_{\oplus }$ (cyan), $h$ (amber) and $r$ (white) sharing Earth's centre as origin.

WHY three symbols and not one? Because gravity is measured from the centre of the Earth, not the surface. So all the physics formulas want $r$ — but engineers quote $h$ because that's what you see. The bridge is simple:

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2. Roundness of the path — $e$ (eccentricity)

Not every orbit is a perfect circle. Most are ellipses — a circle that's been squashed. One number, $e$, measures how squashed. See Figure 2.

Figure 2 — as $e$ grows from 0 (cyan circle) to 0.7 (amber), the ellipse stretches while Earth stays at one focus.

WHY the topic needs $e$: it is the single knob that separates a GEO (needs $e=0$, must hang still) from a Molniya (wants big $e$, so it can loiter far away over the north). No $e$, no orbit types.

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3. The size of the ellipse — $a$, and its two ends $r_a$, $r_p$

An ellipse has a "long way across" and a "short way across". Half the long way is the master size number. See Figure 3.

Figure 3 — perigee $r_p$ and apogee $r_a$ from Earth at the focus; the full span is $2a=r_p+r_a$, with $r_p=a(1-e)$, $r_a=a(1+e)$.

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4. The tilt of the plane — $i$ (inclination)

An orbit lives in a flat plane slicing through Earth's centre. $i$ measures how tilted that plane is compared to the equator. See Figure 4.

Figure 4 — three inclinations: equatorial ($i=0^{\circ }$, cyan), the Molniya critical angle ($i=63^{\circ }$, white), and retrograde SSO-like ($i=98^{\circ }$, amber).

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5. The strength of gravity — $G$, $M$, and the shortcut $\mu$

Gravity's pull depends on two things: how strong gravity is in general, and how heavy the puller is.

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6. Motion in a circle — $v$, $T$, $m$, and the idea of centripetal force

To stay in orbit, a satellite must move. A few symbols describe that motion.

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7. Two kinds of "day" — sidereal vs solar

The parent note insists GEO uses $86164$ s, not $86400$ s. Here is why there are two days at all.

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8. The bulge that ruins perfection — $J_2$

Earth is not a perfect ball; it bulges at the equator. That bulge has a name in the maths.

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How these feed the topic

The deeper machinery each foundation opens: the balance in §6 is fully worked in the Two-Body Problem and the Vis-Viva Equation; the timing law $T^2\propto a^3$ is Kepler's Laws of Planetary Motion; low-orbit consequences appear in Atmospheric Drag and Orbital Decay and Satellite Ground Tracks; and changing $a$ (raising or lowering an orbit) costs energy studied in Hohmann Transfer and Delta-v Budgets.

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Equipment checklist

Cover the right side and test yourself.

Recall Self-test: can you state the core idea in one breath?

Every orbit is one ellipse under gravity; the types just vary its size $a$, stretch $e$, and tilt $i$. Ready? ::: If you answered all checklist items, open the parent note.