Enter orbital decay inputs
This engineering model assumes a circular orbit and an exponential atmosphere. It is useful for screening, trade studies, and comparative mission analysis rather than high-fidelity operational prediction.
Plotly graph
The graph below shows altitude against elapsed time. When you submit the form, the plotted curve updates immediately.
Example data table
| Scenario | Initial Altitude (km) | Mass (kg) | Area (m²) | Cd | Reference Density (kg/m³) | Scale Height (km) | Expected Behavior |
|---|---|---|---|---|---|---|---|
| Small LEO payload | 350 | 120 | 1.4 | 2.1 | 2.789e-10 at 200 km | 60 | Faster decay due to higher drag-to-mass ratio. |
| CubeSat bus | 500 | 40 | 0.25 | 2.3 | 2.789e-10 at 200 km | 60 | Longer residence unless solar activity increases density. |
| Dense bus with small frontal area | 400 | 450 | 0.8 | 2.0 | 2.789e-10 at 200 km | 60 | Slower decay because ballistic coefficient is higher. |
Formula used
1) Atmospheric density model
ρ(h) = ρref × S × exp(-(h - href) / H)
2) Circular orbital velocity
v = √(μ / r), where r = Re + h
3) Drag acceleration
ad = 0.5 × ρ × v² × Cd × A / m
4) Specific orbital energy approach
ε = -μ / (2r)
dε/dt = -ad × v
5) Altitude decay rate for circular orbit
dh/dt ≈ dr/dt = -(2r² / μ) × ad × v
6) Ballistic coefficient
B = m / (Cd × A)
Variable meanings: ρ is atmospheric density, ρref is reference density, S is solar activity factor, H is scale height, μ is Earth’s gravitational parameter, r is orbital radius, Re is Earth radius, Cd is drag coefficient, A is frontal area, and m is spacecraft mass.
This method is a practical engineering approximation. It works best for circular or near-circular low Earth orbits and quick trade studies.
How to use this calculator
- Choose an atmospheric preset or keep custom values.
- Enter the initial orbital altitude and the reentry threshold altitude.
- Provide spacecraft mass, projected frontal area, and drag coefficient.
- Set the reference density, reference altitude, and scale height for your atmosphere model.
- Adjust solar activity factor to reflect quieter or denser upper-atmosphere conditions.
- Enter the integration time step and maximum simulation horizon.
- Press Calculate Orbital Decay to view the lifetime estimate, decay rates, and graph.
- Use the CSV and PDF buttons to export summary metrics and time-series data.
Frequently asked questions
1) What does this orbital decay calculator estimate?
It estimates how atmospheric drag lowers orbital altitude over time. It reports lifetime, drag acceleration, decay rate, ballistic coefficient, orbital velocity, and a plotted descent trend.
2) Is the model suitable for operational collision avoidance?
No. It is intended for engineering screening and comparative analysis. Operational flight dynamics normally use higher-fidelity atmosphere models, tracking data, attitude history, and numerical propagators.
3) Why does solar activity matter here?
Stronger solar activity heats and expands the upper atmosphere. That raises density at a given altitude, increasing drag and usually shortening orbital lifetime.
4) What is the ballistic coefficient telling me?
It measures how resistant the spacecraft is to drag. A higher ballistic coefficient generally means slower decay, because the object has more mass relative to drag-producing area.
5) Why is the orbit assumed circular?
Circular orbit assumptions simplify the energy and drag relationships. That keeps the tool transparent, fast, and practical for concept work, though it reduces fidelity for eccentric trajectories.
6) What should I use for drag coefficient?
Many preliminary studies use values around 2.0 to 2.4 for compact spacecraft in free molecular flow. Use mission-specific aerodynamic or geometry data when available.
7) Why might the result say reentry was not reached?
That usually means the maximum simulation horizon ended first or the drag level is too weak under your selected inputs. Extend the horizon or review the atmosphere settings.
8) Can I export the results?
Yes. After calculation, use the CSV button for a spreadsheet-friendly file or the PDF button for a clean summary report with key metrics and sampled trajectory data.
Engineering notes
This page uses a white-theme layout, a responsive calculator grid, and a stacked single-column page structure. The calculator area itself expands to three columns on large screens, two on medium screens, and one on mobile devices.