Planet Mass from Wobble: Calculating Planetary Weight

1. How is the planet mass from wobble primarily determined using the Radial Velocity method?

By measuring the star's change in temperature

By measuring the amplitude of the star's spectral line shifts

By measuring the diameter of the planet's shadow

By calculating the star's distance from the galactic center

By measuring the planet's orbital speed directly

If a planet orbits a star, it exerts a gravitational tug that causes the star to move around the system's barycenter; if this motion causes a Doppler shift in the star's light, then the magnitude (amplitude) of that shift reveals the velocity of the star, which is used to calculate the planet's mass.

Explanation

If a planet orbits a star, it exerts a gravitational tug that causes the star to move around the system's barycenter; if this motion causes a Doppler shift in the star's light, then the magnitude (amplitude) of that shift reveals the velocity of the star, which is used to calculate the planet's mass.

2. In exoplanet science, a stronger wobble meaning a higher radial velocity semi-amplitude (K) directly indicates a more massive orbiting body, assuming all other orbital parameters are equal.

True

False

If the gravitational force between two bodies is proportional to the product of their masses (F = G * M * m / r^2), then an increase in the planet's mass (m) results in a stronger force on the star; if the force is stronger, then the star's orbital velocity (wobble) must increase.

Explanation

If the gravitational force between two bodies is proportional to the product of their masses (F = G * M * m / r^2), then an increase in the planet's mass (m) results in a stronger force on the star; if the force is stronger, then the star's orbital velocity (wobble) must increase.

3. Which conservation law is the foundation for calculating star motion planet mass interactions?

Conservation of Charge

Conservation of Linear Momentum

Conservation of Angular Momentum

Conservation of Parity

Conservation of Energy only

If we assume the star-planet system is isolated, then the total momentum must remain constant; if the planet moves with a certain momentum in one direction, then the star must move with equal and opposite momentum, allowing us to relate their masses and velocities.

Explanation

If we assume the star-planet system is isolated, then the total momentum must remain constant; if the planet moves with a certain momentum in one direction, then the star must move with equal and opposite momentum, allowing us to relate their masses and velocities.

4. When performing a radial velocity mass calculation, which of the following variables must be known or estimated to find the planet's mass?

The orbital period of the planet (P)

The mass of the host star (M_star)

The velocity semi-amplitude of the star (K)

The radius of the planet

The composition of the star's core

If the simplified mass function is derived from Kepler’s Third Law and Newton’s Law of Gravity, then the calculation requires the period, the star's mass, and the measured stellar velocity; if the planet's radius does not affect the gravitational tug, it is not required for this specific mass calculation.

Explanation

If the simplified mass function is derived from Kepler’s Third Law and Newton’s Law of Gravity, then the calculation requires the period, the star's mass, and the measured stellar velocity; if the planet's radius does not affect the gravitational tug, it is not required for this specific mass calculation.

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5. What is the main limitation of exoplanet mass estimation using the Radial Velocity method alone?

It cannot detect gas giants

It only provides the minimum mass (m sin i)

It only works for stars within 1 light-year

It requires the planet to have an atmosphere

It only works for planets with circular orbits

If the radial velocity method only measures the component of motion along our line of sight, and if we do not know the tilt (inclination) of the orbit, then we cannot know the total velocity; therefore, we can only calculate the minimum mass required to produce the observed wobble.

Explanation

If the radial velocity method only measures the component of motion along our line of sight, and if we do not know the tilt (inclination) of the orbit, then we cannot know the total velocity; therefore, we can only calculate the minimum mass required to produce the observed wobble.

6. The variable 'K', which represents the peak velocity of the stellar wobble in a radial velocity mass calculation, is known as the velocity __________.

If the star moves back and forth in a periodic cycle, and if we measure the maximum velocity relative to the system's center of mass, then that specific value is defined as the velocity semi-amplitude.

Explanation

If the star moves back and forth in a periodic cycle, and if we measure the maximum velocity relative to the system's center of mass, then that specific value is defined as the velocity semi-amplitude.

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7. If a planet's orbital distance (semi-major axis) increases, the planet mass from wobble detection becomes easier because the period is longer.

True

False

If gravitational force follows an inverse-square law, then increasing the distance between the star and planet significantly weakens the gravitational tug; if the tug is weaker, the star's wobble velocity decreases, making it harder to detect.

Explanation

If gravitational force follows an inverse-square law, then increasing the distance between the star and planet significantly weakens the gravitational tug; if the tug is weaker, the star's wobble velocity decreases, making it harder to detect.

8. In a system where the star and planet orbit a barycenter, if the star is 1000 times more massive than the planet, how do their orbital velocities compare?

The star moves 1000 times faster

The planet moves 1000 times faster

They move at the same speed

The star does not move

The planet moves at the speed of light

If the momentum of the system is conserved (M1 * V1 = M2 * V2), and if the star's mass (M1) is 1000 times the planet's mass (M2), then the planet's velocity (V2) must be 1000 times greater than the star's velocity (V1) to balance the equation.

Explanation

If the momentum of the system is conserved (M1 * V1 = M2 * V2), and if the star's mass (M1) is 1000 times the planet's mass (M2), then the planet's velocity (V2) must be 1000 times greater than the star's velocity (V1) to balance the equation.

9. Which of the following would result in a stronger wobble meaning a more detectable signal for astronomers?

A massive planet like Jupiter orbiting very close to its star

A low-mass star (like a Red Dwarf)

A very high orbital inclination (edge-on view)

A planet with a very long orbital period (e.g., 100 years)

A star with a very high mass (like an O-type star)

If the signal strength (K) is proportional to the planet's mass and inversely proportional to the star's mass and the square root of the distance, then a big planet, a small star, and an edge-on alignment (maximizing sin i) all increase the measured wobble.

Explanation

If the signal strength (K) is proportional to the planet's mass and inversely proportional to the star's mass and the square root of the distance, then a big planet, a small star, and an edge-on alignment (maximizing sin i) all increase the measured wobble.

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10. What is the role of the "Inclination (i)" in exoplanet mass estimation?

It determines the planet's temperature

It is the angle between the orbital plane and the line of sight

It is the speed of the star's rotation

It is the distance to the star

It is the planet's density

If we are measuring the star's motion toward or away from Earth, then the angle at which we view the orbit (inclination) dictates how much of the true velocity is visible to us as a Doppler shift.

Explanation

If we are measuring the star's motion toward or away from Earth, then the angle at which we view the orbit (inclination) dictates how much of the true velocity is visible to us as a Doppler shift.

11. To calculate star motion planet mass, astronomers must first determine the mass of the host star, usually by analyzing its spectral type and luminosity.

True

False

If the radial velocity equation for the planet's mass contains the star's mass as a variable (m is proportional to K * M_star^(2/3)), then we cannot solve for the planet's mass without first having a reliable estimate for the star's mass.

Explanation

If the radial velocity equation for the planet's mass contains the star's mass as a variable (m is proportional to K * M_star^(2/3)), then we cannot solve for the planet's mass without first having a reliable estimate for the star's mass.

12. When the orbital inclination (i) is 90 degrees, the exoplanet mass estimation (m sin i) is equal to the ________ mass of the planet.

If sin(90) equals 1, and if the calculation provides "m sin i", then substituting 1 for sin i results in the true physical mass of the planet.

Explanation

If sin(90) equals 1, and if the calculation provides "m sin i", then substituting 1 for sin i results in the true physical mass of the planet.

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13. Why does a "Hot Jupiter" create a much easier planet mass from wobble detection than an "Earth-twin"?

Earth-twins have no gravity

Hot Jupiters are closer to the star, creating a higher frequency and higher amplitude tug

The Sun prevents us from seeing Earth-twins

Earth-twins only orbit white dwarfs

Hot Jupiters are made of reflective gold

If a planet is both massive and in a tight orbit, the gravitational force is maximized and the cycle repeats often; if the force is high and frequent, the resulting stellar velocity (K) is large enough to be easily measured above instrument noise.

Explanation

If a planet is both massive and in a tight orbit, the gravitational force is maximized and the cycle repeats often; if the force is high and frequent, the resulting stellar velocity (K) is large enough to be easily measured above instrument noise.

14. In Grade 12 radial velocity astronomy, what can be inferred if the radial velocity curve is not a perfect sine wave but is instead "spiky" or skewed?

The orbit is highly eccentric (elliptical)

The planet is rotating very fast

There are multiple planets in the system

The star is expanding and contracting

The orbit is a perfect circle

If an orbit is circular, the velocity change is smooth and sinusoidal; if the orbit is elliptical, the planet speeds up at periastron, causing a sharp change in the star's velocity; if multiple planets pull on the star, their individual sine waves add together into a complex, skewed pattern.

Explanation

If an orbit is circular, the velocity change is smooth and sinusoidal; if the orbit is elliptical, the planet speeds up at periastron, causing a sharp change in the star's velocity; if multiple planets pull on the star, their individual sine waves add together into a complex, skewed pattern.

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15. What happens to the semi-amplitude (K) of the star motion planet mass signal if we keep the planet the same but double the mass of the host star?

K increases

K decreases

K stays the same

K becomes zero

K doubles

If the star's velocity (K) is inversely proportional to the star's mass (specifically M_star^(-2/3)), then increasing the star's mass makes it "heavier" and harder for the planet to move; therefore, the amplitude of the wobble decreases.

Explanation

If the star's velocity (K) is inversely proportional to the star's mass (specifically M_star^(-2/3)), then increasing the star's mass makes it "heavier" and harder for the planet to move; therefore, the amplitude of the wobble decreases.

16. The radial velocity mass calculation is independent of the distance between the Earth and the star system.

True

False

If the Doppler shift measures the velocity of the star, and if velocity is an intrinsic property of the star's motion, then the percentage shift in wavelength remains the same regardless of whether the star is 10 or 100 light-years away (provided it is bright enough to see).

Explanation

If the Doppler shift measures the velocity of the star, and if velocity is an intrinsic property of the star's motion, then the percentage shift in wavelength remains the same regardless of whether the star is 10 or 100 light-years away (provided it is bright enough to see).

17. In the equation for exoplanet mass estimation, if we don't know the inclination, the calculated value is technically a __________ limit for the planet's mass.

If the measured velocity is V_observed = V_true * sin i, and if sin i is always less than or equal to 1, then V_true must be equal to or greater than V_observed; therefore, the calculated mass is the lowest possible mass the planet could have.

Explanation

If the measured velocity is V_observed = V_true * sin i, and if sin i is always less than or equal to 1, then V_true must be equal to or greater than V_observed; therefore, the calculated mass is the lowest possible mass the planet could have.

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18. Which of the following units is most commonly used to express the velocity semi-amplitude (K) in modern planet mass from wobble studies?

Kilometers per hour

Meters per second

Light years per day

Astronomical Units per year

Degrees per second

If the wobbles caused by Earth-like planets are tiny, and if current state-of-the-art spectrographs can detect shifts as small as 10-50 cm/s, then meters per second (m/s) is the standard unit used for these high-precision measurements.

Explanation

If the wobbles caused by Earth-like planets are tiny, and if current state-of-the-art spectrographs can detect shifts as small as 10-50 cm/s, then meters per second (m/s) is the standard unit used for these high-precision measurements.

19. What are the requirements for a star to be a good candidate for radial velocity mass calculation?

The star must have many sharp absorption lines

The star must be relatively "quiet" (low stellar activity/spots)

The star must be rotating very slowly

The star must be a Pulsar

The star must be in a different galaxy

If the method relies on measuring tiny shifts in spectral lines, the lines must be sharp and stable; if the star is active or rotating fast, the lines become blurred (broadened), which masks the subtle Doppler shifts caused by a planet.

Explanation

If the method relies on measuring tiny shifts in spectral lines, the lines must be sharp and stable; if the star is active or rotating fast, the lines become blurred (broadened), which masks the subtle Doppler shifts caused by a planet.

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20. If a stronger wobble meaning higher K is observed in a star identical to the Sun, but the period is the same as Earth's (1 year), what can we conclude about the planet?

It is further away than Earth

It is more massive than Earth

It is smaller than Earth

It is a "rogue planet"

It has no atmosphere

If the period (P) and star mass (M) are the same, the distance (a) must also be the same; if the distance is the same but the star's velocity (K) is higher, the only remaining variable that can cause a stronger tug is a higher planet mass.

Explanation

If the period (P) and star mass (M) are the same, the distance (a) must also be the same; if the distance is the same but the star's velocity (K) is higher, the only remaining variable that can cause a stronger tug is a higher planet mass.

Measuring the Heavyweights: Planet Mass from Wobble Quiz

1. How is the planet mass from wobble primarily determined using the Radial Velocity method?

2.

What first name or nickname would you like us to use?

2. In exoplanet science, a stronger wobble meaning a higher radial velocity semi-amplitude (K) directly indicates a more massive orbiting body, assuming all other orbital parameters are equal.

3. Which conservation law is the foundation for calculating star motion planet mass interactions?

4. When performing a radial velocity mass calculation, which of the following variables must be known or estimated to find the planet's mass?

5. What is the main limitation of exoplanet mass estimation using the Radial Velocity method alone?

6. The variable 'K', which represents the peak velocity of the stellar wobble in a radial velocity mass calculation, is known as the velocity __________.

7. If a planet's orbital distance (semi-major axis) increases, the planet mass from wobble detection becomes easier because the period is longer.

8. In a system where the star and planet orbit a barycenter, if the star is 1000 times more massive than the planet, how do their orbital velocities compare?

9. Which of the following would result in a stronger wobble meaning a more detectable signal for astronomers?

10. What is the role of the "Inclination (i)" in exoplanet mass estimation?

11. To calculate star motion planet mass, astronomers must first determine the mass of the host star, usually by analyzing its spectral type and luminosity.

12. When the orbital inclination (i) is 90 degrees, the exoplanet mass estimation (m sin i) is equal to the ________ mass of the planet.

13. Why does a "Hot Jupiter" create a much easier planet mass from wobble detection than an "Earth-twin"?

14. In Grade 12 radial velocity astronomy, what can be inferred if the radial velocity curve is not a perfect sine wave but is instead "spiky" or skewed?

15. What happens to the semi-amplitude (K) of the star motion planet mass signal if we keep the planet the same but double the mass of the host star?

16. The radial velocity mass calculation is independent of the distance between the Earth and the star system.

17. In the equation for exoplanet mass estimation, if we don't know the inclination, the calculated value is technically a __________ limit for the planet's mass.

18. Which of the following units is most commonly used to express the velocity semi-amplitude (K) in modern planet mass from wobble studies?

19. What are the requirements for a star to be a good candidate for radial velocity mass calculation?

20. If a stronger wobble meaning higher K is observed in a star identical to the Sun, but the period is the same as Earth's (1 year), what can we conclude about the planet?