Satellite Orbit Simulator

Satellite Orbit Simulator

Simulate the orbit of a satellite around Earth by adjusting parameters such as mass, velocity, and launch angle. Observe the satellite's trajectory and live telemetry data in real-time.

2D Earth Gravity Simulator

Satellite Configuration

0° = Towards Earth, 90° = Tangent Up

Simulation Settings

Live Telemetry

Velocity: 0.00 km/s
Heading: 0.0°
Altitude: 0.0 km

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Simulator Overview

This satellite orbit simulator is a specialized software tool to predict, visualize, and analyze the movement of an object around the Earth. The simulator solves the equations of motion to precisely determine a satellite's spatial coordinates at any given time.

Mathematical Propagation

The primary function of this simulator is orbital propagation, which utilizes a satellite's initial state, position and velocity, to compute its future trajectory. This simulator is constrained to a two-body model, applying Newton’s laws of motion and universal gravitation to simulate an idealized elliptical orbit.

Notice that this simulator does not use more complex perturbation modeling. Real-world orbits are much more complex since they account for Earth’s J2 effect, atmospheric drag, solar radiation pressure, and third-body gravity from the Moon and Sun.

The physics

In this simulator, the equations of motion are utilized to define the satellite's orbital trajectory. This simulation processes the satellite's current state to computationally determine its subsequent position at the next tick time interval.

Newton’s Laws

Simulators primarily rely on Newton’s Law of Universal Gravitation. The fundamental equation used to find the force F acting on a satellite is:

F = G(Mm/r2)

The simulator then uses Newton’s Second Law (F=ma) to find the satellite's acceleration. By combining these, we get the fundamental differential equation for orbital motion:

r¨ = −(μ/​r3)r

The acceleration (r¨) of the satellite is always pointing toward the center of the Earth and is determined by the "gravitational parameter" (μ = GM) and the distance (r).

The Motion

Since the satellite is constantly moving, r (the distance) is constantly changing, which means the force is also constantly changing. The calculation must be calculated tick by tick.

Calculating tick by tick

This simulator uses a method that is called Cowell’s Method:

  1. Start: Look at the satellite's current position and velocity.
  2. Calculate Force: Use the gravity formula to find the current acceleration.
  3. Tick Forward: Move the satellite forward by a tick step.
  4. Update: Calculate the new position and velocity based on that acceleration.
  5. Repeat: Do this repeatedly to draw the full orbit.

Configuration

This simulator allows you to change the satellites mass, initial velocity, and launch angle.

The simulation settings allows you to change the time speed of the simulation from 0x (paused) to 10x (10 times normal speed).

Live Telemetry

Actual orbital telemetry represents the observational truth of a satellite's behavior. Live telemetry consists of a real-time data stream transmitted from the spacecraft to a ground station, detailing its current operational status. While a simulator generates mathematical predictions of a satellite's expected location, live telemetry provides empirical measurements of its true position and active performance.

The simulator’s live telemetry

The live telemetry of this simulator uses the calculations of the position of the satellite’s motion and position, and displays them for visual assistance. The live telemetry in this simulator displays the current velocity, heading (angle of path), and altitude of the satellite.

Velocity (v)

This is the satellite's velocity vector. It tells you how fast the satellite is covering ground.

If the satellite's velocity components are (vx,vy,vz), the speed is:

v = √(vx2 + vy2 + vz2)

Heading (Flight Path Angle (γ))

The heading reported in telemetry is usually the Flight Path Angle. This is arguably the most important number for understanding if an orbit is stable. It is the angle between the satellite’s velocity vector and the "tangent up" (a line perpendicular to the Earth).

The simulator finds this by comparing the position vector (r) and the velocity vector (v) using a dot product:

sin(γ) = r * v / ​∣r∣ * ∣v∣

Altitude (r)

In this simulator we measure the altitude or Geocentric Radius, the distance from the center of the Earth to the center of the satellite.

The simulator takes the 2D coordinates (x,y) and uses the 2D distance formula:

r = √(x2 + y2)

Note that this telemetry shows altitude (r) for just the simulation of the object and does not represent earth to accurate scale. Realistic simulators may use Altitude (h) and include the third dimension for coordinates (x,y,z) and its respective formula. To get the altitude (h), the simulator subtracts the Earth's radius (RE ≈ 6,371 km) from the distance:

h = r − RE