Starshade Occulter Sizing Calculator

Introduction to Starshade Occulter Sizing

A starshade occulter is a carefully shaped screen that flies far in front of a space telescope so the telescope can look for faint planets next to bright stars. In a direct-imaging mission, the occulter blocks most of the starlight before it reaches the telescope, leaving a darker field where a planet, a dust ring, or another dim feature may be easier to detect. This calculator gives a first-pass estimate of the starshade diameter needed for a chosen observing wavelength, a chosen separation between the telescope and the starshade, and a target inner working angle, often shortened to IWA. In plain language, the inner working angle is the smallest apparent angle from the star at which the system can start to see something nearby.

The tool is intentionally simplified for starshade sizing, because real mission studies include petal-shape optimization, broadband diffraction control, alignment tolerances, deployment errors, and formation-flying limits. Even so, a compact sizing relation is useful because it reveals how the hardware scales. If you increase the wavelength, the required diameter rises. If you increase the separation, the required diameter also rises in this calculator’s geometry. If you ask for a smaller inner working angle so planets closer to the star become visible, the starshade needs to grow again. Those are the core tradeoffs this page is meant to make obvious.

This calculator is most useful for early concept exploration, classroom demonstrations, and rough mission comparisons. It is not a final optical design tool, but it captures the main first-order scaling that drives starshade size. That makes it a practical way to build intuition before moving on to detailed diffraction simulations or mission analyses. Because the result depends on a tight interplay between wavelength, formation distance, and angular requirement, even small unit mistakes can lead to a very different answer. The sections below walk through the variables in that same order so the calculation is easier to sanity-check.

How to Use the Starshade Occulter Sizing Calculator

Enter the three mission inputs in the form below to estimate a starshade occulter diameter. Observation wavelength is entered in nanometers, which is convenient for visible and near-infrared astronomy. A value around 500 to 550 nm represents green visible light, while larger values such as 800 to 1000 nm move into the red and near-infrared. Starshade-telescope separation is entered in kilometers because these systems are usually spaced by tens of thousands of kilometers. The desired inner working angle is entered in milliarcseconds, a very small angular unit commonly used in astronomy.

After you click Compute Diameter, the calculator converts the values into SI units, applies the sizing equation, and reports the required starshade diameter in meters. The summary box gives the main result in a compact form, and the reference table records the latest input and output values for an easy check. If you want to save the result, use the copy button that appears after a successful calculation. The table is not a separate model; it simply mirrors the values used for the current run.

A good way to learn from the tool is to vary one input at a time while keeping the other two fixed. Hold separation and inner working angle steady, then increase wavelength to see the diameter estimate climb. Next, keep wavelength and angle fixed while changing separation to see how formation distance affects the occulter size. Finally, adjust the inner working angle to represent a more or less ambitious science goal and watch the result move in the opposite direction. This one-variable-at-a-time approach makes the starshade trade space much easier to understand and helps identify which assumption drives a mission comparison.

The Starshade Occulter Sizing Formula

The starshade occulter sizing relation used here is a first-order geometric scaling rule that connects wavelength, separation, and inner working angle to an estimated diameter. The formula is shown in MathML so the variables remain readable in supporting browsers and assistive technology, and the script underneath evaluates the same relation directly. It is an approximation for quick sizing rather than a full diffraction model, but it is valuable because it makes the direction of every tradeoff explicit.

The inner working angle in radians is treated as the angular scale the occulter must support. With the approximation implemented on this page, the relation is:

Formula: θ = (2 λ Z) / D_s

Here is wavelength, is starshade diameter, and is separation between the starshade and telescope. Rearranging gives the diameter estimate used by the script:

Formula: D_s = (2 λ Z) / θ

To make the inputs practical, the calculator converts wavelength from nanometers to meters and converts inner working angle from milliarcseconds to radians. The angular conversion starts with:

Formula: 1 arcsec = π / 648000 rad

Since the input field uses milliarcseconds, the next step is:

Formula: 1 mas = 10^−3 arcsec

The wavelength field is also converted before the diameter is calculated:

Formula: λ = λ_nm × 10^−9 m

Once those unit conversions are complete, the script computes diameter directly in meters. Read the result as a quick sizing estimate for a starshade occulter. It describes the approximate scale of hardware needed to support the requested observing geometry, not the final petal design, edge profile, deployment behavior, or suppression performance across a broad spectral band. If the number changes substantially when you nudge an input, the mission may be operating near a demanding corner of the trade space.

Interpreting Starshade Inputs and Diameter Results

Each starshade occulter input has a clear physical meaning. Wavelength represents the color of light you want to observe. Longer wavelengths generally push the estimated diameter upward because the calculator scales directly with wavelength. Separation is the distance between the telescope and the starshade. In this calculator, a larger separation also pushes the diameter upward, so formation geometry is part of the size estimate rather than something that cancels out. The inner working angle is the science requirement: smaller values mean the mission can look closer to the star, which is especially important when trying to image planets in compact habitable zones.

The output diameter is best read as a design-scale number. It is a quick answer that helps compare observing concepts, not a flight-ready specification. If the result seems unexpectedly small or unexpectedly large, check the units first. Confusion between arcseconds and milliarcseconds, or between kilometers and meters, can change the answer by orders of magnitude. It is also worth remembering that the calculator uses a simplified scaling relation, so the output is only as good as the assumptions you provide. A result that seems too aggressive is often the right moment to revisit the observing band or the requested angular reach.

Another useful way to read the result is by direction of change. Tightening the inner working angle increases the required diameter, while relaxing it lowers the estimate. Moving to a longer wavelength grows the diameter, and increasing separation grows it as well. These trends are why the calculator is helpful during early mission brainstorming: it shows which lever matters most before a team commits to a detailed study. In practice, the most demanding science case usually sets the scale, while less demanding cases become easier to satisfy once the baseline diameter is known.

Worked Example: Checking Starshade Occulter Scaling

A practical starshade occulter worked example starts with the default 500 nm wavelength, a 50,000 km separation, and a 100 mas inner working angle. Entering those values produces an estimate of about 206,265 m using this page’s deliberately simple formula. That large figure is not a proposal for a flight article; it is a useful prompt to inspect the assumptions and the strong effect of angular units. It demonstrates why first-pass models should lead into, rather than replace, an optical and systems-engineering study.

Next, keep the wavelength and separation fixed but change the inner working angle from 100 mas to 50 mas. Because the angle is in the denominator, halving it doubles the estimated diameter. Alternatively, return the angle to 100 mas and increase wavelength from 500 nm to 1000 nm. The estimate doubles again because wavelength is in the numerator. Finally, double separation and the estimate also doubles. These simple comparisons are more informative than chasing one magical input set because they expose the proportional relationships directly.

This comparison approach is especially helpful when reviewing mission options. A science team may want to see planets close to nearby stars, but that goal can be expressed through a smaller angular limit, a different observing band, or a different formation distance. The calculator reveals the size consequence of each choice. If one choice produces an occulter that is much harder to package, deploy, or fly, that choice is usually the limiting constraint that deserves a second look first.

Limitations and Assumptions of Starshade Occulter Sizing

This starshade occulter sizing calculator is intentionally simplified, so it should not be used as a substitute for a full optical design study. Real starshades are not plain circular disks. They use carefully optimized petal shapes to control diffraction over a range of wavelengths, and their performance depends on edge accuracy, petal count, manufacturing quality, and alignment with the telescope. The simple diameter relation used here does not model those details. It is best thought of as a first-order screening tool that helps a team decide whether an idea is worth deeper analysis.

Another starshade sizing limitation is that the result is monochromatic in spirit even though the wavelength input can be changed freely. Real observations often span a band of wavelengths, and a starshade sized for one wavelength may not deliver the same performance at much longer wavelengths. Engineers commonly add margin after a quick estimate to account for broadband behavior, alignment uncertainty, and practical deployment constraints. The important point is that this margin belongs in the engineering conversation after the initial calculation, not before it.

The tool also does not estimate fuel use, slew time between targets, telescope aperture effects, throughput, achievable contrast, or formation-flying control authority. Those factors matter enormously in mission planning. What this page provides is a transparent first-order answer to a foundational question: for a chosen observing wavelength, separation, and inner working angle, about how large does the starshade occulter need to be? That answer can still identify whether a concept is comfortably sized, uncomfortably large, or incompatible with the rest of a mission design.

Why a Starshade Occulter Trade Study Matters

Direct imaging of exoplanets is one of the hardest tasks in observational astronomy because stars are overwhelmingly brighter than the planets orbiting them. A starshade occulter offers one path around that problem by blocking starlight before it enters the telescope, rather than trying to remove it entirely inside the telescope with internal optics. That difference is why starshades remain attractive in mission studies even though they require precision formation flying over enormous distances. The basic sizing question matters because the shade has to be large enough to do its job without becoming impractical to launch and operate.

The numbers produced by this calculator connect abstract science goals to physical hardware. If a science team wants to detect Earth-like planets close to nearby Sun-like stars, that requirement translates into a small inner working angle. A smaller angular limit then pushes the design toward a larger starshade or a different separation. Once those values are visible, launch packaging, deployment reliability, target-to-target travel time, and mission lifetime become easier to discuss. The result is a more grounded conversation about what a mission can afford in size, distance, and observing flexibility.

That is why even a simplified starshade occulter calculation has value. Students can use it to learn how diffraction and angular resolution interact. Researchers can use it for quick back-of-the-envelope checks. Enthusiasts can use it to appreciate why future exoplanet missions are so ambitious. In every case, the result is a clearer sense of the scale and challenge of building a giant spaceborne occulter. Use the estimate to compare assumptions, catch unit errors early, and decide which concept deserves a more realistic diffraction simulation next.