Measuring the Shadow: Transit Depth Explained Quiz

If a planet passes in front of a star and blocks its light, and if both objects are viewed as circular disks from our perspective, then the amount of light lost (the depth) must be proportional to the cross-sectional area of the planet's disk compared to the star's disk.

If the depth of the dip represents the fraction of total light blocked, and if we assume the light is emitted uniformly from the star's surface, then a 1% decrease in received light requires that 1% of the star's surface area is obstructed by the planet.

If the area of a circle is calculated by the formula πr^2, and if depth is the ratio of the planet's area (πRp^2) to the star's area (πRs^2), then the π symbols cancel out, leaving the ratio of the radii squared.

If the transit depth depends on the square of the planet's radius, and if Jupiter's radius is roughly 11 times larger than Earth's, then Jupiter will block significantly more starlight, making the signal much easier for telescopes to distinguish from background noise.

If the depth is defined by the physical area ratio (Rp/Rs)^2, then only the physical dimensions of the planet and the star determine how much light is blocked; the distance to Earth affects total brightness but not the percentage of light lost.

If the star's radius (Rs) is the denominator in the depth formula (Rp/Rs)^2, and if that denominator increases while the planet's radius stays the same, then the resulting fraction (the depth) must become a smaller value.

If transit depth is an area ratio of the planet to the star, and if both objects appear smaller at the exact same rate as distance increases, then the ratio of their relative areas remains constant regardless of how far away the system is from the observer.

If an Earth-sized planet blocks only about 0.008% of a Sun-like star's light, and if decimals are difficult to represent in graphs, then astronomers use "parts per million" to describe these tiny changes as whole numbers (e.g., 80 ppm).

If the depth is calculated as the square of the radius ratio (0.1^2), and if 0.1 multiplied by 0.1 equals 0.01, then the resulting transit depth is 0.01, which is equivalent to a 1% drop in brightness.

If the light curve only provides the relative ratio of the sizes, then we must independently know the star's actual size (often determined by its temperature and color) to convert that ratio into a physical measurement like kilometers.

If a Red Dwarf is physically small, then a planet of a fixed size will occupy a larger percentage of its total surface area; if it occupies a larger percentage, it blocks a greater portion of the light and creates a deeper dip.

If we are inferring the dimensions of a planet based on the amount of starlight it obstructs rather than measuring the planet's diameter directly in an image, then the scientific method is classified as indirect.

If planets are generally much smaller than stars, and if even a giant like Jupiter only blocks about 1% of the Sun's light, then a massive 50% drop suggests the blocking object is nearly the same size as the star, indicating a binary star system.

If the depth formula is (Rp / Rs)^2, then the depth can only increase if the numerator (Rp) gets larger or the denominator (Rs) gets smaller; orbital distance and mass (without a change in size) do not affect the blocked area.

If M-dwarfs (Red Dwarfs) have significantly smaller radii than Sun-like stars, and if a planet's radius is a larger fraction of a small star than a large one, then the resulting transit dip will be much deeper and easier for instruments to see.

If the area of a circle is calculated using the square of the radius (r^2), then the relationship is quadratic; if you double the radius (2r), the area—and thus the transit depth—increases by four times (2^2 = 4).

If a light curve shows the brightness relative to its normal state (where normal is set at 1.0 or 100%), then the dips are measured as a decrease from that baseline, which is known as relative flux.

If a planet only crosses the edge of the star, it never fully enters the stellar disk; if it is never fully in front of the star, it never reaches its maximum potential blockage, resulting in a shallow, V-shaped curve instead of a flat-bottomed one.

If the star isn't perfectly uniform or the planet has extra features like rings, the amount of light blocked will be slightly different than a simple disk model predicts, leading to slightly different calculated values for the planet's radius.

If Earth's radius is ~6,371 km and the Sun's is ~696,340 km, the radius ratio is approx 0.01; if we square 0.01 (0.01 * 0.01), the result is 0.0001 (or 0.01%), which is the tiny fraction of sunlight Earth blocks.