Week 2: Gravity and the Doppler Shift

Question 1

How is the gravitational force between two objects impacted by change in their mass and the distance between them? Include the mathematical calculations for distance.

Answer 1

gravity increases with mass and decreases with distance
distance impacts gravity with inverse square law
- 2X distance apart means 4x less gravity
- 3x distance apart means 9x less gravity

Question 2

What is the center of mass? How is it affected by the mass of the objects? Include mathematical calculations.

Answer 2

balance point between two objects where the effect of gravity operates
closer to object with greater mass
mass of object 1 is 10x greater than object 2 -> center of mass is 10x closer to object 1

Question 3

How does an exoplanet impact the motion of the star it orbits?

Answer 3

center of mass is closer to star, but not at its center -> star spins periodically with exoplanet

Question 4

What is reflex motion? How is it detected?

Answer 4

spinning of a star around the center of mass between it and a planet (motion caused by gravity of exoplanet)
detected through looking at changes in the light emitted by stars

Question 5

How does the energy of light affect its wavelength and color?

Answer 5

low energy = longer wavelengths = redder color
high energy = shorter wavelengths = bluer color

Question 6

What wavelengths (numbers) are red and blue light generally around?

Answer 6

red = 700nm
blue = 400nm

Question 7

How does the movement of an object impact its wavelength and how that wavelength is measured?

Answer 7

wavelength doesn’t change!!
but how we perceive it changes
wave in front of movement is compressed
wave behind movement is spread out

Question 8

What is the Doppler effect?

Answer 8

apparent shift in wavelength of light or sound as perceived by the observer or an approaching or receding body
motion away causes light to be redshifted
motion approaching causes light to be blueshifted
indicates a star rotating due to the gravity of an exoplanet

Question 9

define the radial velocity method. what data is gathered to use this method?

Answer 9

method for finding exoplanets which measures the Doppler shift in the light emitted by a star to detect reflex motion caused by the gravity of the planet
found by looking at the spectrum of the star over time

Question 10

How is the magnitude of a stars Doppler shift related to it’s radial velocity?

Answer 10

directly proportional to each other
higher magnitude of Doppler shift is higher magnitude of radial velocity

Question 11

What is a spectrum? What is important about the absorption lines?

Answer 11

Spectrum is a representation of the total light emitted by an object ordered by wavelength
Absorption likes are unique to a certain element

Question 12

What element of detecting a Doppler shift is performed in a lab?

Answer 12

Compare the observed spectrum of a star with one made in a lab with the same materials (spectrum made in lab is zero point which star spectrum is compared to)

Question 13

True or false: the radial velocity method is very precise.

Answer 13

True! we can make super precise measurements and calculations for this method

Question 14

What are four limitations of the radial velocity method?

Answer 14

Larger planets are easier to detect (too small planets make light shifts imperceptible)
Shorter orbital distance easier to detect (too high orbital distance means radial velocity is smaller and harder to detect)
only tells us mass of planet instead of size (can’t determine density!!)
orbital inclination - we can’t detect movement towards or away from us if the system is oriented so that the sun moves but not towards or away from us
introduces uncertainty to measurements

Question 15

True or false: the radial velocity method can be used to detect multiple exoplanets in the same system at once.

Answer 15

true!

Question 16

What is the transit method?

Answer 16

monitors starlight to detect periodic dimming, which indicates an exoplanet blocking part of the star when it passes in front of it every orbit
also known as eclipse method

Question 17

How does the orbital plane of an exoplanet system affect the ability of its exoplanets to be discovered using the transit method?

Answer 17

we have to be facing the sun’s equator (exoplanet must pass in front of sun each orbit from our perspective)

Question 18

True or false: it is easy to see eclipses with the transit method.

Answer 18

kind of false
eclipses happen for a short period of time in comparison to the planet’s length of orbit
we need to look at a lot of stars at once to detect eclipses because they are so rare!!

Question 19

How does the size of the dip in brightness of a star relate to the size of the exoplanet orbiting it?

Answer 19

deeper dip = larger exoplanet

Question 20

In the transit method, what happens when the exoplanet passes behind its host star?

Answer 20

small dip in the brightness of the star
exoplanets reflect light from the star, so when the exoplanet is hidden from view there is less light coming in our direction from the system

Question 21

True or false: the transit method can be used to detect multiple exoplanets around the same star at once.

Answer 21

true

Question 22

What planet types are the easiest to discover with the radial velocity and transit methods?

Answer 22

hot jupiters are easiest to find with both

Question 23

What are the three main limitations of the transit method?

Answer 23

01 size of exoplanet - if it is too small, the dip in starlight can be imperceptible
02 orbital distance - if exoplanet is too far away from its host star, the amount of light it blocks each orbit can be imperceptible
03 orbital inclination - this method only works when star systems are between a specific range of angles in comparison to where we are viewing them from

Question 24

What is kepler’s first law of planetary motion?

Answer 24

planets move in elliptical orbits with the host star at one focus of the ellipse

Question 25

What is kepler’s second law of planetary motion?

Answer 25

a line connecting a planet and its host star sweeps out equal areas in equal times as the planet moves through its orbit

Question 26

What is kepler’s third law of planetary motion?

Answer 26

the cube of the period of the planet is proportional to the square of the semi-major axis (which represents the average distance of the planet from the star)
p = orbital period
a = orbital distance
p^2 = a^3

Question 27

How does one find the velocity of an exoplanet?

Answer 27

use kepler’s 3rd law of planetary motion to find orbital distance and data from the radial velocity method to find orbital period
(2π * orbital distance) / orbital period

Question 28

What is transit depth? How is it calculated?

Answer 28

how much starlight is dimmed when an exoplanet eclipses its host star
(B_beforeTransit - B_duringTransit) / B_beforeTransit

Question 28

How does one find the mass of a planet?

Answer 28

find velocity with kepler’s third law of planetary motion and data from radial velocity method
radial velocity is determined through observation
m_planet = (M_star * V_star) / V_planet

Question 28

How does one find the radius of an exoplanet?

Answer 28

find transit depth from transit method data
r_planet = R_star(square root of transit depth)

Question 29

How does one find the density of an exoplanet?

Answer 29

find radius from transit method data (use transit depth and equation)
find mass from radial velocity method from velocity
density = m_planet / ((4/3)πr^3_planet)

Question 29

how is density different from mass?

Answer 29

density is the amount of mass per unit of volume of a substance
mass is the amount that an object resists acceleration

Question 30

What are the drawbacks of calculating planet density from radial velocity and transit method data?

Answer 30

we can only calculate mean density from this data
this could indicate multiple different planet compositions so we can’t be certain about any composition inferences we make from those calculations

Question 31

what is comparative planetology?

Answer 31

studying the planets in our solar system to come up with general rules for planetary structure, which we can then hopefully apply to exoplanets

Question 32

Why is it difficult to detect exoplanets through just looking closely at stars?

Answer 32

exoplanets can be up to billions of times fainter than their host stars (don’t produce their own light, so light coming from them is all reflected from their host star)
exoplanets can appear to be really close to their host star when viewing from far away

Question 33

How does the direct imaging method work?

Answer 33

first block out the light from a star and then directly look for an exoplanet around it that reflects the star’s light

Question 34

under what conditions does direct imaging work best?

Answer 34

with longer wavelengths (near infrared) rather than visible light
with big planets close to their parent star (reflect more light = more easily visible)
repeated observation of a star over years

Question 35

what is a coronagraph?

Answer 35

instrument that blocks out the center circle of its view
used to look for exoplanets with direct imaging method (star’s light is blocked out)

Question 36

How does gravitational lensing work?

Answer 36

large objects warp spacetime
when a large object (a star) passes in front of another star, the behind star’s light’s trajectory is warped so that it appears brighter from out perspective
when the front star has an exoplanet, we can see a small period of the light from the behind star seeming even brighter each orbit

Question 37

What are the pros and cons of gravitational lensing?

Answer 37

pros:
works equally well for planets that are close to use vs far away, large vs small, large orbital distance vs small
- unlike the other methods which are better for close large planets with short orbital distances
cons:
microlensing events are very rare!! (space is mostly empty)
- have to observe a lot of stars at once for a chance at seeing this

Question 38

What is a selection effect from the doppler method?

Answer 38

we can’t be sure what angle a system is at compared to where we are viewing it from -> measurements have some uncertainty

Question 39

what is a selection effect from the eclipse method?

Answer 39

only works at very specific inclinations -> we can only detect a small fraction of total exoplanets with this method