What will you learn in this guide?
- Explaining free fall in orbit
- Using circular-orbit relations with the correct radius
- Linking the type of orbit to a mission’s observation needs
Climbing to where gravity ends is not enough
A vehicle in orbit has not escaped gravity. Gravity keeps changing the direction of its velocity and holds it on a curved path. A vehicle moving with the right horizontal speed falls, but the planet’s surface curves away beneath it at the same time. Reaching orbit therefore does not just mean climbing very high; it also means building up enough speed, in the right direction, at the right position.
On an elliptical orbit the point closest to the central body is called periapsis and the farthest point apoapsis; for Earth the terms perigee and apogee are also used. According to Kepler’s law of areas, a body moves faster when it is close to the centre and slower when it is far away. That is why points you mark at equal time intervals on a diagram are not evenly spaced; the gaps in the visualisation are a direct clue to the speed.
Two simple relations, two important limits
For a circular orbit the speed can be calculated as v = √(μ/r) and the period as T = 2π√(r³/μ). μ is the gravitational parameter of the central body and r is the orbital radius measured from its centre. If an altitude h above the surface is given, Earth’s radius must be added first. Using a μ in metres with an r in kilometres produces a result that looks plausible but is badly wrong.
These expressions belong to the ideal two-body approximation. The atmosphere, Earth’s not-quite-spherical shape, the effects of the Sun and Moon and other perturbing forces are ignored. Applying the circular-orbit formula to every point of an ellipse is not correct. Seeing in a teaching simulation that circular speed falls and the period lengthens as altitude increases is a good starting point for understanding real mission dynamics.
Sources: [3]
An orbit is a mission decision
Low Earth orbit offers close-up observation and short link distances, while continuous coverage of a region may require different architectures. A geostationary satellite sits on a circular orbit above the equator, moving with Earth’s rotation, and appears almost fixed from the ground. Sun-synchronous orbits help observe a region at similar local solar times, which makes images from different dates easier to compare.
A useful way to understand a manoeuvre is to follow the orbit’s later shape, not just the instantaneous speed reading. A short, ideal speed increase in the direction of motion at periapsis can raise apoapsis. The fact that cruising speed is lower on a higher circular orbit does not mean no energy is needed to get there. First define the goal, the reference frame and the starting orbit; then study the effect of the manoeuvre along the whole path. The models here are designed to make physical principles visible, not for mission operations.
- Altitude h and distance from the centre r are different things.
- The two-body model is an approximation; it does not give live satellite positions.
- The same image scale may not represent the physical size of different orbits.
Practice: read motion together with scale
On a teaching sketch, mark the planet’s centre, its surface and two different circular orbits. For each orbit, write the distance from the centre and the altitude above the surface separately. Now add points showing equal time intervals and compare the motion of the vehicle on the inner orbit with the one on the outer orbit. Placing the same number of points purely for visual symmetry can be misleading. Stating the physical duration clearly is at least as important as colour and animation for an animated infographic to be understood correctly. Do not assume that every second on screen corresponds to a real second.
Next, turn one of the circles into an ellipse and label the nearest and farthest points. Discuss why an animation moving at constant speed may not represent elliptical motion correctly. In the description of any simulation, look separately for the model used, the time scale and the display scale. Real satellite tracking and a conceptual demonstration can look similar but require different data. Making this distinction supports being a good reader of science and building clear, honest explanations in future teaching visuals.
Model and equations
v = √(μ/r) ; T = 2π√(r³/μ)
Ideal circular orbit
Units: μ: m³/s²; r: m; v: m/s; T: s
Model limit: two-body, circular-orbit assumption. r is measured from the planet’s centre. This is not a live ephemeris or an operational flight solution.
At a glance
- Orbit
- Orbital motion can be explained as continuous free fall under gravity.
Interactive lab: altitude, speed and period
The simulator opens on the geostationary preset: at an altitude of 35,786 km the circular speed is 3.07 km/s and one orbit takes 23.9 hours; because the spacecraft goes round in the same time as Earth turns, it stays above the same spot in the animation. Then press the ISS preset: the speed rises to 7.66 km/s and one orbit shrinks to 92.8 minutes. Note that the simulator measures the radius from Earth’s centre, r = R + h.