When Light Curves Throw Us Curve Balls

Background

This fall the NASA Lucy Mission will begin its 12-year journey to investigate a record-breaking eight asteroids in the first-ever mission to the Trojan asteroids—a population of small bodies that lead and follow Jupiter in its orbit around the Sun. Many asteroids (especially small ones) have interesting, irregular shapes. But as these asteroids are both small (less than 100 miles or 160 km wide) and very far away (hundreds of millions of miles or kilometers) they appear as unresolved points of light, even when viewed using our largest Earth-based and Earth-orbiting telescopes. Consequently, we won't know for sure what these asteroids look like until the Lucy spacecraft flies by these enigmatic bodies in 2027-2033. However, that won't stop us from working to collect as many clues as possible about these bodies today, from here on Earth.

One of the few ways scientists can try to estimate an asteroid's shape from an extreme distance is by looking at its light curve—i.e., examining how bright the asteroid is and how that brightness changes with time. As an irregularly shaped asteroid spins, the amount of light it reflects changes. If you watch an asteroid long enough, the brightness changes repeat, and that repeating light curve can help scientists determine its rotation speed and its shape. And if you watch the asteroid even longer, the light curve can change as the Earth and asteroid orbit around the Sun, revealing how the asteroid is oriented in space.

However, the relationship of a light curve to the asteroid shape is not necessarily unique. Asteroids of different shapes could generate indistinguishable light curves.

Objectives

Your challenge is to develop a tool that allows users to explore how the shape of an asteroid affects the appearance of its light curve.

Note that many celestial objects have light curves; as you are researching this topic you may come across discussions of light curves of binary stars, transiting exoplanets, and other stellar objects like supernovae. This challenge focuses on the (visible) light curves of asteroids that are illuminated by reflected sunlight—not on self-luminous objects.

Potential Considerations

As you develop your tool, you may (but are not required to) consider the following:

• Some useful definitions:
• Light Curve - A graph that shows the brightness of an object over a period of time
• Shape Model - A 3D model of an object (like an asteroid)
• Rotational Phase – A number (from zero to one) representing the angle in a periodic pattern
• There are a number of properties that affect the appearance of a light curve including the rotation rate and axis of rotation, shape, surface texture, and variations in surface reflectance (albedo). You likely only want to consider a few of these as variables.
• There are numerous online programs (including both proprietary and open source) that render 3D shape models and allow you to illuminate the objects with a defined light source. Potential search terms include: 3D modeling, 3D rendering, and ray tracing.
• One way to turn a resolved image of a 3D model into a point for a light curve is to render a resolved image and then add up the brightness of the pixels in the image; just make sure that you only illuminate the 3D object from a single direction (sometimes called a "Sun" light) without ambient light (i.e., on a black background).
• A matte (Lambertian) reflectance is a fine assumption for the surface of the asteroids. If you want to use a more complex model, see the papers in the example resources.
• If you are not familiar with 3D modeling software, you can also generate light curves in the real world with an object, a light source, and a camera!
• You might start by examining the light curves of simple ellipsoids (a sphere has a rather dull light curve) then explore what happens with the more complex shapes of real or imagined asteroids.
• While the main focus is asteroids, feel free to have fun with the concept. For example, your tool could allow users to upload their own 3D model of a teapot and see what that light curve would look like!
• As it is often impossible to observe an asteroid continually over a single rotation, scientists take advantage of the fact that asteroid light curves often repeat themselves each rotation. By using this repetition they can "fold" the data and plot it as a function of the rotational phase instead of time. However, as the seasons change on the body the light curve may change.
• To take this challenge to the next level, you could make a tool that allows users to modify the shape of an object or add brightness variations to the object’s surface to make it match an existing light curve.
• Potential keywords you can search include: 3D asteroid models, asteroid light curve databases, asteroid lightcurve photometry database

For data and resources related to this challenge, refer to the Resources tab at the top of the page. More resources may be added before the hackathon begins.

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