Astronomy Quiz | Applied Questions on Eclipses, Seasons, Planetary Orbits and Exoplanet Detection

The Moon's orbital plane is tilted by about five degrees relative to Earth's orbital plane. Consequently, at most new moons the Moon passes above or below the Sun and its shadow misses Earth. A solar eclipse requires not only a new moon but also sufficiently close alignment near a point where the two orbital planes intersect.

The seasons are caused primarily by the tilt of Earth's axis. A hemisphere tilted toward the Sun has a higher solar elevation and longer daylight, increasing the solar energy received per unit area. The fact that the hemispheres have opposite seasons, and that Earth is not near perihelion during Northern Hemisphere summer, rules out Earth-Sun distance as the main cause.

The Moon is in synchronous rotation: it rotates once in approximately the same 27-day period that it takes to orbit Earth. It therefore keeps nearly the same hemisphere facing Earth. If the Moon did not rotate, different parts of its surface would face Earth as it moved around its orbit, so seeing the same side does not mean that the Moon fails to rotate.

Kepler's second law states that a line joining a planet and the Sun sweeps out equal areas in equal times. Near perihelion, the planet must move faster along its orbit to sweep out the same area, so in the same 30 days it travels farther than it does near aphelion. Motion along an elliptical orbit is not uniform in speed.

For bodies orbiting the same star, Kepler's third law states that the square of the orbital period is proportional to the cube of the semi-major axis. B therefore has a longer period than A. The condition that the planets orbit the same central body matters; planets around stars of different masses cannot always be compared using only this simple relationship.

Earth follows an inner orbit with a shorter period than Mars. As Earth overtakes Mars, the direction from the moving Earth toward Mars changes, making Mars temporarily appear to move backward against the distant stars. This is an effect of the relative motions of the two planets and the observer; neither Mars's orbital direction nor its rotation reverses.

With Earth's orbit providing the same observing baseline, a closer object shows a larger apparent change in direction, or annual parallax. A is therefore closer than B. In real measurements, a star also has proper motion, so observations at multiple times are used to separate that steady motion from the periodic parallax signal.

A shift of known spectral lines toward shorter wavelengths is a blueshift. Under the Doppler interpretation specified here, it indicates a component of motion toward the observer. A redshift toward longer wavelengths would indicate recession. This measurement alone does not directly determine the transverse component of velocity across the sky.

The interval between repeated transits indicates the orbital period, so both periods are about 20 days. For equal-sized stars and similar transit paths, a deeper dip means that a larger fraction of the stellar disk is blocked, implying that A has a larger planetary radius. Transit depth alone does not directly determine a planet's mass or its orbital distance.

Periodic dimming is a strong planet-candidate signal, but an eclipsing stellar companion, a background source, dust or an instrumental artifact can produce a similar pattern. Scientists should reexamine the images and light curve and use independent evidence, such as radial-velocity measurements, to eliminate alternatives. Repetition alone does not exclude every false positive.