The Hertzsprung–Russell Diagram - Astronomy: A Beginner ...motion by F = ma. In astronomy, force...

ASTR 102 Lecture Slides – The H‐R Diagram and the Laws of Motion

Dr. Kristin B. Whitson 1

• H–R diagram plots stellar luminosity against surface temperature

• Luminosity ranges 10-4–104 L

The Hertzsprung–Russell Diagram

Luminosity ranges 10 10 L .

• Temperature

– ranges by a factor of 10

– increases to the left

– spectral sequence OBAFGKM puts hottestOBAFGKM puts hottest (blue) on left, coolest (red) on right

• Can compare properties of stars using this diagram

• Stars are not uniformly distributed.

The Main Sequence

• Most stars lie in a well-defined band called the Main Sequence.

– Cool stars tend to be faint

– Hot stars tend to be bright

• Of the 80 closest stars, most are on the Main Sequence, including the Sun



• Stellar radii vary on the Main Sequence – dashed lines show constant stellar radius

same R different L and T

Stellar Radii on the H-R Diagram

– same R, different L and T

– radius-luminosity-temperature relationship: L % T4

• Faint, red, cool, M-type stars

– ≤ 0.1 R

– called red dwarfs

• Bright, blue, hot, O-type stars

– ~ 10 or greater R

– called blue giants

• 100 brightest stars

– All more luminous than Sun

– All are giants (red or blue).

Luminosity on the Main Sequence

• Giants are easy to detect

– Rare: O and B supergiants< 0.01% of all stars

– Blue giants = top left.

• Dwarfs are hard to detect

– Red Dwarfs (bottom right)probably most common: > 80% of all stars



• White dwarfs do not lie on the Main Sequence:

– Very hot

White Dwarf Region

– Dim

– Small

– Bottom left on H-R

• ~ 9% of all stars are white dwarfs

• Hard to detect

• Red giants – to the top right of the Main Sequence.

– Cooler than Sun

Red Giant Region

– Luminosity range: 50 –10,000 L

– 5-500 R

• Relatively rare: 1% of all stars.



– Main sequence, red giant regions evident.

f hit d f

The Hertzsprung–Russell Diagram• Hipparcos measured colors and luminosities of > 2,000,000 stars.

– few white dwarfs

• Overall distribution of stars in space: 90% main sequence, 9% white dwarfs, 1% red giants

– Presumably same ratio everywhere in the universey

• Sun is average by luminosity, temperature, radius

– Middle of H-R

Luminosity Class• Spectral line widths of main sequence, red giants, white dwarfs differ

due to pressure and density of star

• Less dense atmosphere narrower lines

• Luminosity classes designate the type of star by its spectral line width

– Red giant main sequence white dwarf

• Correlates pressure of star with luminosity.



Standard Luminosity Classes

Position of luminosity classes on the H-R Diagram

• Determination of the star’s luminosity class reveals the kind of star (dwarf, giant, main sequence).

• Sun = G2V

– G2 spectral type

– V class luminosity

• All stars of spectral class K2 have surface temperature ~ 4500 K and show the same spectral lines.

Determining Luminosity from Stellar Spectra

• Width of spectral lines reveal the luminosity class (K2Ib, K2V, etc.)

• Read luminosity directly from H-R diagram based on spectral and luminosity class



• Astronomical distances measured by techniques valid over certain ranges

Distance Measurement Techniques

• Radar ranging for solid objects < 0.000005 pc away

• Stellar parallax

– Distance determination by measuring apparent shift of star from two vantage points

– Objects ≤ 200 pc away

• Spectroscopic parallax

– Uses spectroscopy and luminosity classes to find distance

– Has nothing to do with parallax

– Useful for stars ≤ 10,000 pc away

Spectroscopic ParallaxSpectroscopic parallax is the application of the mathematical relationship between luminosity, apparent brightness, and distance

Step 1: Measure the star’s apparent magnitude and spectral class

• Apparent magnitude: amount of energy detected on a 1 m2 surface in 1 second put it on the magnitude scale.

• Spectral class: t h t t lmatch to spectral

class OBAFGKM and luminosity class (I-V)



Spectroscopic ParallaxStep 2: Use spectral / luminosity class to estimate luminosity from H-R diagram and correlate it with the absolute magnitude

⎟⎟⎠

⎞⎜⎜⎝

⎛=−

pc 10distance log 5magnitude absolute magnitudeapparent 10

What is the distance to a star of apparent

Step 3: Apply the distance/magnitude relationship

ppmagnitude 10 and class A0V?

How Do We Determine a Star’s Mass?• A star’s mass is measured by observing its gravitational influence on a

nearby body (another star or a nearby planet).

• If distance between two orbiting bodies is known use Newton’s Laws to calculate their masses.

• Sir Isaac Newton (1642-1727) and his “law of universal gravitation”

– Hit on the head by a falling apple

OR

– Comparing the accelerations of the planets and the Moon.



Newton’s First Law of Motion(a) An object at rest will

remain at rest

(b) An object in motion stays in motion in a straight line at constant speed

(c) Unless an external force acts on it.

• Also called the Law of Inertia

• Inertia: the tendency of an object to resist fa change in its state of motion

– to stay at rest

– to maintain state of motion in a straight line

Newton’s First Law of Motion

The ball is guided around the metal rim. When the ball leaves the rim, which path (1, 2, or 3) will the ball follow?

• Earth’s inertia causes it to travel in a straight line

• Sun’s gravitational force pulls Earth toward it

• Result: Earth travels in a curved path. How fast?



Newton’s Laws of Motion• An object’s inertia is directly related to its mass

– More mass– Less mass

– Easier to tackle

• Force: a quantity capable of producing motion

– “Unless an external force acts” refers to the net force

– Harder to move– Can change

directions faster

• If an object’s velocity changes it undergoes an acceleration.

Slows downSpeeds upChanges direction

Newton’s Second Law of Motion• Newton realized to produce an

acceleration, a force must be acting.

• Acceleration produced by a force on an• Acceleration produced by a force on an object is directly proportional to the magnitude of the force

– Greater net force = greater acceleration

• Acceleration is inversely proportional to the mass of the objectthe mass of the object

– Greater mass = smaller acceleration

maF mFa =→=



• On Earth, acceleration due to Earth’s gravity is ~9.8 m/s2 everywhere, at all

The 2nd Law of Motion and Gravity• If you know initial conditions and forces, can determine object’s state of

motion by F = ma. In astronomy, force is most always gravity.

gravity is 9.8 m/s everywhere, at all times, and on everything

– directed toward center of Earth

• On the Moon, acceleration due to Moon’s gravity is ~ 1.6 m/s2 (1/6th of Earth)

F f it i l b– Force of gravity is less because Moon’s mass is less

– It would take less force to put an object into orbit

Newton’s Law of Universal Gravitation

Every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them

G: universal gravitational constant – valid throughout the universeG = 6.67 x 10-11 N.m2/kg2



Gm m

• At locations equidistant from Sun’s center, gravitational force due to Sun is the same and directed toward the Sun

Newton’s Law of Universal Gravitation

Gm1m2

r2F = • If m1 or m2 increases and distance stays the same: force increases

• The strength of the Sun’s gravitational pull decreases in proportion to the square of the distance from the Sun

• Force of gravity can never equal zero, no matter the distance.

• When object A exerts a force on object B, object B exerts an equal and opposite force on object A.

For every action there is an equal and

Newton’s Third Law of Motion

A B

For every action there is an equal and opposite reaction.

• Gravity: if student jumps off a table, she accelerates toward Earth. Newton’s third law states that BOTH the student and Earth accelerate toward each other.

– Student: small mass, large acceleration (m1a1)

– Earth: huge mass, very small acceleration (-m2a2)

– m1a1 = -m2a2 : forces are equal and opposite



Gravitational pull of Earth

Newton’s Third Law of Motion

• Mutual gravitational attraction of Sun and planets is what keeps the planets moving in stable elliptical orbits.

Gravitational pull of Sun

– 3rd law: Forces on Sun/Earth are equal

elliptical orbits.

Why does the Sun dominate the interaction?

– 3 law: Forces on Sun/Earth are equal

– 2nd law: F = ma or a = F/m

– Acceleration is inversely proportional to its mass

– Sun accelerates 300,000X less because it is 300,000X more massive than Earth

Measuring Mass using Orbital Motion• All masses are calculated in astronomy using only the speed of

something orbiting the object (measure circumference and time), and the path of the orbit (for the radius)

• Consider the case of extreme difference in mass (Sun-planet):

– Force required to keep an object moving in a circle is centripetal force, given by:

– Equate with universal law of gravitation:

mpv2

rF =

mv2

rF =

= FGmpms

r2=

GMs

rv2 =

r rv2

rGms

r2=

rv2

GM =



Weighing the SunThe Earth orbits the Sun at ~30 km/s at a distance of 150,000,000 km. What is the mass of the Sun?

The Hertzsprung–Russell Diagram - Astronomy: A Beginner ...motion by F = ma. In astronomy, force...

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