Example Data Table
| System |
Central mass |
Orbiting mass |
Semi-major axis |
Eccentricity |
Approx period |
| Sun and Earth |
1 solar mass |
1 earth mass |
1 AU |
0.0167 |
365.26 days |
| Sun and Mars |
1 solar mass |
0.107 earth masses |
1.523679 AU |
0.0934 |
686.98 days |
| Earth and Moon |
1 earth mass |
1 lunar mass |
384400 km |
0.0549 |
27.32 days |
Formula Used
The calculator uses Newtonian two-body motion. The standard gravitational parameter is:
μ = G(M + m)
Here, G is the gravitational constant. M is the central mass. m is the orbiting body mass.
The orbital period is calculated with:
T = 2π √(a³ / μ)
The closest and farthest orbital distances are:
rp = a(1 - e) and ra = a(1 + e)
Speed at any selected orbital radius uses the vis-viva equation:
v = √[μ(2 / r - 1 / a)]
Specific orbital energy is:
ε = -μ / (2a)
Specific angular momentum is:
h = √[μa(1 - e²)]
How to Use This Calculator
Select a preset or enter custom mass and distance values. Choose matching units for each input. Enter eccentricity between 0 and 1. Use 0 for a circular path. Add a true anomaly angle to inspect speed and radius at a specific point in the orbit.
Choose output units for distance and time. Press the calculate button. The result table appears above the form and below the header. Use CSV for spreadsheet work. Use PDF for a compact saved report.
Newtonian Orbit Calculation Guide
Why Newtonian Orbits Matter
Newtonian orbit calculation turns gravity into a practical model. It links mass, distance, speed, and time. The method assumes two bodies. One body is central. The second body travels around it. This simple view still explains many useful cases.
Main Inputs
The calculator starts with the gravitational parameter. It uses the central mass and the orbiting mass. The semi major axis sets the main orbit size. Eccentricity sets the shape. A value of zero gives a circle. Larger values create a longer ellipse. The true anomaly shows the current angle from periapsis.
Reading the Results
Several results describe the same orbit from different sides. Period shows the time needed for one revolution. Mean motion shows angular progress per second. Periapsis and apoapsis show the closest and farthest distances. The vis viva equation gives speed at any selected point. It also explains why a planet moves faster near periapsis.
Energy and Momentum
Energy is also important. A bound elliptical orbit has negative specific orbital energy. More negative energy means the body is more tightly held. Specific angular momentum shows how strongly the body sweeps area. It stays constant in the ideal two body model. This follows Newtonian motion and conservation laws.
Practical Use
The tool is useful for lessons, estimates, and comparisons. You can compare Earth, Mars, or a satellite case. You can change distance units and mass units. The results update after submission. The export buttons help save the current study. The example table gives reference values for common systems.
Limits of the Model
Real spaceflight can need more detail. Other planets can disturb the orbit. Atmospheres can slow low satellites. Radiation pressure can affect tiny objects. Relativity matters near very massive bodies. Yet Newtonian laws remain a strong first model. They give fast answers with clear formulas. They also help students understand why orbital speed, period, and distance are connected. Use reasonable inputs. Keep eccentricity below one for elliptical paths. Check units before comparing results. Then read the result table as a compact orbit report.
Advanced Checks
Advanced users can test design choices. A wider orbit gives a longer period. A heavier central body gives higher speed. A larger eccentricity creates a sharper speed difference. These patterns make the table valuable for quick checks, classroom demonstrations, and early mission sketches or deeper numerical simulation later.
FAQs
What does this calculator estimate?
It estimates two-body orbital properties using Newtonian gravity. It returns period, speed, distance, energy, angular momentum, anomalies, and gravitational force.
Can I use it for satellites?
Yes. Enter the planet as the central mass. Enter the satellite mass and semi-major axis. For low satellites, remember that drag is not included.
What eccentricity should I enter?
Use 0 for a circle. Use a value between 0 and 1 for an ellipse. Higher values create more stretched orbital paths.
Why is periapsis speed higher?
The orbiting body moves faster near the central body because gravitational potential energy is lower there. The vis-viva equation shows this speed change.
Does orbiting mass matter?
It matters in the exact two-body parameter. For small planets around stars, its effect is tiny. For similar masses, it becomes important.
What is true anomaly?
True anomaly is the angle from periapsis to the body's current position. It helps calculate radius and speed at one selected point.
Why is specific orbital energy negative?
A negative value means the body is bound to the central mass. It does not have enough energy to escape in the ideal model.
Is this suitable for real mission design?
It is suitable for early estimates and study. Real mission design needs perturbations, atmosphere, precise ephemerides, and numerical integration.