Astronomy: Detecting Exoplanets: Transit and Radial Velocity Worksheet

Question 1

A star's brightness drops by 1 percent every 10 days, and each drop lasts about 3 hours. What detection method is being used, and what does the repeating drop in brightness suggest?

Accepted Answer

The transit method is being used. The repeating drop in brightness suggests that a planet passes in front of the star once every 10 days as seen from Earth.

Question 2

In a transit light curve, what does the depth of the dip mainly tell astronomers about the planet?

Accepted Answer

The depth of the dip mainly tells astronomers the planet's size compared with the star. A deeper dip usually means the planet blocks more starlight and has a larger radius.

Question 3

A planet transiting a Sun-sized star causes the star's light to decrease by 0.01, or 1 percent. Use transit depth = (planet radius / star radius)^2 to find the planet's radius compared with the star's radius.

Accepted Answer

The planet radius divided by the star radius is the square root of 0.01, which is 0.10. The planet's radius is 0.10 times the star's radius.

Question 4

A light curve shows transit dips at day 4, day 16, day 28, and day 40. What is the orbital period of the planet?

Accepted Answer

The orbital period is 12 days because each transit occurs 12 days after the previous one.

Question 5

Two planets orbit identical stars. Planet A causes a 0.5 percent transit dip. Planet B causes a 2 percent transit dip. Which planet is larger, and how do you know?

Accepted Answer

Planet B is larger because it causes a deeper transit dip. A deeper dip means the planet blocks a larger fraction of the star's light.

Question 6

Why can the transit method miss many planets even if they really orbit other stars?

Accepted Answer

The transit method can miss many planets because the planet's orbit must be aligned so that the planet crosses in front of the star from Earth's point of view. If the orbit is tilted too much, no transit is visible.

Question 7

A star's spectral lines shift slightly toward blue, then later toward red, in a repeating pattern. What detection method is being used, and what motion of the star is being measured?

Accepted Answer

The radial velocity method is being used. Astronomers are measuring the star's motion toward and away from Earth caused by the gravitational pull of an orbiting planet.

Question 8

What is the Doppler effect, and why is it important for detecting exoplanets with radial velocity?

Accepted Answer

The Doppler effect is the change in observed wavelength caused by motion toward or away from an observer. It is important because tiny wavelength shifts reveal that a star is wobbling due to an orbiting planet.

Question 9

A star shows a radial velocity pattern that repeats every 6.2 days. What does this period represent for the planet?

Accepted Answer

The 6.2 day period represents the planet's orbital period, because the star's wobble repeats once for each complete orbit of the planet.

Question 10

Planet X causes its star to wobble with a maximum radial velocity of 2 meters per second. Planet Y orbits an identical star at the same distance and causes a maximum radial velocity of 20 meters per second. Which planet is likely more massive, and why?

Accepted Answer

Planet Y is likely more massive because it causes a larger stellar wobble. For identical stars and similar orbits, a more massive planet pulls more strongly on its star.

Question 11

A transit is observed every 30 days, but the radial velocity signal of the same star is very small. Give one possible reason the radial velocity signal is small.

Accepted Answer

One possible reason is that the planet has a low mass, so it pulls only weakly on the star. Another possible reason is that the star is massive, making its motion harder to detect.

Question 12

Explain how using both transit and radial velocity measurements can help astronomers learn more about an exoplanet than either method alone.

Accepted Answer

Transit measurements can give the planet's radius, while radial velocity measurements can give information about the planet's mass. Together, mass and radius can be used to estimate density and infer whether the planet may be rocky, icy, or gas-rich.

Question 13

A planet has a mass of 6 Earth masses and a radius of 2 Earth radii. Compared with Earth, its density is mass divided by radius cubed: 6 / 2^3. Calculate its density compared with Earth's density.

Accepted Answer

The density compared with Earth is 6 / 8, which equals 0.75. The planet's average density is about 0.75 times Earth's density.

Question 14

The graph of a star's radial velocity is a smooth wave crossing from positive to negative values and back again. What do the positive and negative values usually represent?

Accepted Answer

The positive and negative values usually represent the star moving away from Earth and toward Earth along our line of sight. The repeating pattern shows the star wobbling as it orbits the system's center of mass.

Question 15

A light curve shows one shallow dip that never repeats during a 90 day observation. Explain why astronomers would be cautious about claiming they found a planet.

Accepted Answer

Astronomers would be cautious because a single dip may be caused by noise, another star, or an instrument effect. Repeating transits with the same shape and spacing provide stronger evidence for an orbiting planet.

Astronomy: Detecting Exoplanets: Transit and Radial Velocity

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