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Densities of worlds

The average density of a body equals its mass divided by its volume. For a sphere, density is:

density = mass 4 3 π R 3

Astronomers can measure both mass and radius accurately when a spacecraft flies by a body.

Using the information in this chapter, we can calculate the approximate average density of the Moon.

Solution

For a sphere,

density = mass 4 3 π R 3 = 7.35 × 10 22 kg 4.2 × 5.2 × 10 18 m 3 = 3.4 × 10 3 kg/m 3

[link] gives a value of 3.3 g/cm 3 , which is 3.3 × 10 3 kg/m 3 .

Check your learning

Using the information in this chapter, calculate the average density of Mercury. Show your work. Does your calculation agree with the figure we give in this chapter?

Answer:

density = mass 4 3 π R 3 = 3.3 × 10 23 kg 4.2 × 1.45 × 10 19 m 3 = 5.4 × 10 3 kg/m 3

That matches the value given in [link] when g/cm 3 is converted into kg/m 3 .

Got questions? Get instant answers now!

Mercury’s strange rotation

Visual studies of Mercury ’s indistinct surface markings were once thought to indicate that the planet kept one face to the Sun (as the Moon does to Earth). Thus, for many years, it was widely believed that Mercury’s rotation period was equal to its revolution period of 88 days, making one side perpetually hot while the other was always cold.

Radar observations of Mercury in the mid-1960s, however, showed conclusively that Mercury does not keep one side fixed toward the Sun. If a planet is turning, one side seems to be approaching Earth while the other is moving away from it. The resulting Doppler shift spreads or broadens the precise transmitted radar-wave frequency into a range of frequencies in the reflected signal ( [link] ). The degree of broadening provides an exact measurement of the rotation rate of the planet.

Doppler radar measures rotation.

Illustration of How Doppler Radar Measures Rotation. At left is a drawing of a portion of the Earth, with an oversized radar dish on the surface pointing upward toward a target planet to the right. A transmitted signal is drawn leaving the dish toward the planet. The reflected signal from the planet is shown as five arrows pointing back in the direction of Earth. At far right are four panels plotting radar intensity versus frequency, with frequency increasing toward the right. The upper panel, labeled “Transmitted signal”, shows the transmitted signal as a tall, narrow spike. The panel below, labeled “Return with no rotation”, plots the return signal if the target planet did not rotate: it is a tall, narrow spike just like the transmitted signal. The next panel is labeled “Return with slow rotation”. This curve is wider at the base and not as tall as the previous curves. The bottom panel is labeled “Return with faster rotation”. This curve is very wide at the base and much shorter than the previous plots.
When a radar beam is reflected from a rotating planet, the motion of one side of the planet’s disk toward us and the other side away from us causes Doppler shifts in the reflected signal. The effect is to cause both a redshift and a blueshift, widening the spread of frequencies in the radio beam.

Mercury’s period of rotation (how long it takes to turn with respect to the distant stars) is 59 days, which is just two-thirds of the planet’s period of revolution. Subsequently, astronomers found that a situation where the spin and the orbit of a planet (its year) are in a 2:3 ratio turns out to be stable. (See [link] for more on the effects of having such a long day on Mercury.)

Mercury, being close to the Sun, is very hot on its daylight side; but because it has no appreciable atmosphere, it gets surprisingly cold during the long nights. The temperature on the surface climbs to 700 K (430 °C) at noontime. After sunset, however, the temperature drops, reaching 100 K (–170 °C) just before dawn. (It is even colder in craters near the poles that receive no sunlight at all.) The range in temperature on Mercury is thus 600 K (or 600 °C), a greater difference than on any other planet.

What a difference a day makes

Mercury rotates three times for each two orbits around the Sun. It is the only planet that exhibits this relationship between its spin and its orbit, and there are some interesting consequences for any observers who might someday be stationed on the surface of Mercury.

Here on Earth, we take for granted that days are much shorter than years. Therefore, the two astronomical ways of defining the local “day”—how long the planet takes to rotate and how long the Sun takes to return to the same position in the sky—are the same on Earth for most practical purposes. But this is not the case on Mercury. While Mercury rotates (spins once) in 59 Earth days, the time for the Sun to return to the same place in Mercury’s sky turns out to be two Mercury years, or 176 Earth days. (Note that this result is not intuitively obvious, so don’t be upset if you didn’t come up with it.) Thus, if one day at noon a Mercury explorer suggests to her companion that they should meet at noon the next day, this could mean a very long time apart!

To make things even more interesting, recall that Mercury has an eccentric orbit, meaning that its distance from the Sun varies significantly during each mercurian year. By Kepler’s law, the planet moves fastest in its orbit when closest to the Sun. Let’s examine how this affects the way we would see the Sun in the sky during one 176-Earth-day cycle. We’ll look at the situation as if we were standing on the surface of Mercury in the center of a giant basin that astronomers call Caloris ( [link] ).

At the location of Caloris, Mercury is most distant from the Sun at sunrise; this means the rising Sun looks smaller in the sky (although still more than twice the size it appears from Earth). As the Sun rises higher and higher, it looks bigger and bigger; Mercury is now getting closer to the Sun in its eccentric orbit. At the same time, the apparent motion of the Sun slows down as Mercury’s faster motion in orbit begins to catch up with its rotation.

At noon, the Sun is now three times larger than it looks from Earth and hangs almost motionless in the sky. As the afternoon wears on, the Sun appears smaller and smaller, and moves faster and faster in the sky. At sunset, a full Mercury year (or 88 Earth days after sunrise), the Sun is back to its smallest apparent size as it dips out of sight. Then it takes another Mercury year before the Sun rises again. (By the way, sunrises and sunsets are much more sudden on Mercury, since there is no atmosphere to bend or scatter the rays of sunlight.)

Astronomers call locations like the Caloris Basin the “hot longitudes” on Mercury because the Sun is closest to the planet at noon, just when it is lingering overhead for many Earth days. This makes these areas the hottest places on Mercury.

We bring all this up not because the exact details of this scenario are so important but to illustrate how many of the things we take for granted on Earth are not the same on other worlds. As we’ve mentioned before, one of the best things about taking an astronomy class should be ridding you forever of any “Earth chauvinism” you might have. The way things are on our planet is just one of the many ways nature can arrange reality.

Questions & Answers

what is the definitions of planet
Mitrajit Reply
A celestial body orbiting around a star
Asim
How to appear for MCQ in this app
nitisha Reply
I l don't understand questions
Nkateko Reply
which quesrions?
Ankit
let it be
nitisha
How to make a telescope
Amit Reply
***youtube.com/channel/UClBN_RpR5X8IdrARwnaL3fg
Steve
***wikihow.com/Make-a-Telescope
Jennifer
optical mechanics
Astro
aptical
Nkateko
Which one has the ring
Isaac Reply
Saturn venue and even Jupiter all have rings the rings on Jupiter, however, aren't so easily noticed due to them only being viable through infrared
Hunter
visible *
Hunter
they each have three rings but not as you might think just think of them all as one big ring because that's basically what they are but they are desperate individual rings
Hunter
separate*
Hunter
can you tell me what is a quantam elighment? Lets see how many people give write answers
gdjm Reply
can you tell me what is a fomalhaut?
gdjm
Fomalhaut Is The Brightest Star In The Constalellation Of Piscis Austrinus.....
Adam
joe.
Tracy
Do You Mean Quantum Entanglement?
Adam
yes
gdjm
No Adam fomalhaut mean eye of universe
gdjm
quantum entanglement is when a husband has been married so long to his wife that he is directly influenced by her action usually in an opposite way. 🤣
Jocofranc
It Is Also The Brightest Star Of The The Constalellation Of Piscis Austrinus.....
Adam
who was the first person to get to the planet
Isaac
can anyone tell me daily rotation of the sun in tokyo
Liridona Reply
tokyo has it's own personal sun
Tracy
can you send me any pictures of the tokyo sun
Liridona
sure! ig?
Tracy
here can u?
Liridona
no it wont let me sadly
Tracy
or
Liridona
snapchat
Liridona
i dont have snapchat 😰
Tracy
okay ig
Liridona
my ig is fatwigga37 if you'd like to see :)
Tracy
Can we use SI units in the equation of Kepler's third law?
Naiyu Reply
can u tell the equation pls
sasmita
how does religion enters to this topic when god created this world
Sakira
How Do You Know A God Created Our Planet?
Adam
you must read bible
Sakira
u must the bible
Sakira
How Do You That Book Is Authentic? And I Have Read The Bible, The Koran, The Torah And The Urantia.....
Adam
The law is T^2 is proportional to R^3 where t is planet's time period and r is average of semi major axis and semi minor axis. Also,don't turn this place into a religious warzone. We already have idiots fighting about religion.
priyanshu
If I Had A Book That Said Insects Created The Universe, Would That Make It Fact?
Adam
Have You Ever Heard Of The Council Of Nicaea?
Adam
Through Out History Mankind Has Worshipped Over 5000 Different Gods, How Do You Know Christ Is The True God?
Adam
God Is A Hypothesis..... The Definition Of Faith Is Belief Without Proof.....
Adam
Thank You Prianshu Roy, This Is A Forum For Science Not Archaic Stories Written By Sheep Herders, Well Said.....
Adam
Hebrew 13:1
onome
P2 = a3
Adam
So You Quote A Bible Verse, Now What?
Adam
Science Discourse Nothing Else.....
Adam
god is real he's not just a wise guess
Sakira
god bless you
Sakira
u know what,u are not here if god werent there!
Sakira
Science Discourse, Nothing Else.....
Adam
Thier Are Many Religious Sites You Can Go To, To Discuss God.....
Adam
hahahaha
Sakira
Have A Great Day.....
Adam
night time here
Sakira
Look Up The Definition Of Day, Instead Of Trying To Look Witty, Again Have A Great Day.....
Adam
😈😈😈
Sakira
such an socratic person?
Sakira
What Was Your Intention In Stating "Night Time Here" ?
Adam
please don't fight over silly stuffs!
Romancho
tangina mo
Sakira
No I Don't Believe A God Exist, But I Will Fight For Your Right To Worship Any God You Wish.....
Adam
no fighting
Sakira
But This Venue Is For Science Discourse.....
Adam
i know!
Sakira
No Fighting, Just Discussion.....
Adam
yes Naiyu, we have to use SI unit in the equation for the Kepler's every laws
Madhav
Thanks.
Naiyu
wow
Kenneth
Tell me about nebula
Asim
How it is created
Asim
Its a dust cloud of hydrogen
Asim
Hello
Asim
a nebula is usually formed when a star ends its life cycle
Chris
Ok
Asim
And its working?
Asim
When the time comes, most stars run out of available hydrogen they have for nuclear fusion
Chris
When that happens there is no more equilibrium between pressure and gravity
Chris
So there is no more pressure to balance the gravitational force, therefore a star collapses into its own core, and then the amount of matter inside the core is so large that the star explodes into a nebula
Chris
its a beautiful view, but very dangerous, the amount of radation is really big
Chris
Look it up on google, there are explanations better than mine
Chris
Ok thanks
Asim
yes ok ?
Jenny
what is your zodiac ?
Jenny
yes I can see mine ?
Jenny
Can anyone tell me in simple terms what's gravity.
Aryan
Gravity is the force that is formed due to the big mass of an object. The bigger is the mass, the bigger is the gravity. That is why the Earth attracts humans or small things. If We were bigger than the planet Earth we would have attracted it.
Lemisa
ha ha
Mahesh
why laughing?
Lemisa
Tell me about white dwarf and red dwarf in simple words
Asim
you have google , youTube and other apps which can help you with those I guess, don't you?🤔
Lemisa
Lemisa you know adam
Asim
yeah
Lemisa
even though I am not sure if you are thinking for the think I am right now...
Lemisa
for the thing I meant
Lemisa
for the love of satan shut up
Tracy
There is no love of Satan !
Lemisa
well that was rude and uncalled for
Calab
satan can suck my nips
Tracy
I can be satan for you Tracy.
Aryan
i wouldnt mind
Tracy
That's so nice of you!
Aryan
even nicer of you to be my dark lord ;)
Tracy
🙃
Aryan
i wouldn't mind
Aryan
that wasn't a question mark that was an emoji but this app doesn't accept emojis
Aryan
yah if i could use emojis id make a bj emoji
Tracy
nice
Aryan
would you like to talk more on my insta nayra_lawragga_pvt
Aryan
That escalated quickly
Steve
what's the scene of voyager 1,did we get any information through it
Aarushi Reply
we are getting a lot of info yet more to be received check official mission report from the officials site ....
Ganeshan
what are the best astronomy books?
neehar Reply
what is the parallel space?
neehar
A brief history of time
Asim
planet and stars by Jay M. Pasachoff skyguide by wimmer chartrand
Minireet
how to measure the brightness of a star in w\m^2
Aarushi Reply
it's based on the percentage of helium I think
neehar
ok TQ😊
Aarushi
it's based planet colour and brightness which called lumiosity
gdjm
Are there planets that has the same characteristics as earth.
Nito Reply
yes ofcourse there are earth like planets but they aren't completely like earth.still scientists have a hope of life existence in there.
Aarushi
yeah of course example is Mars but they only discover water at mars
neehar
there's a much possibility of presence of earth like planets in the universe if they were present at goldilock zones
Jashwanth
what are goldilock zones?
Aarushi
why yes there are planets just like earth out there somewhere we know that much for sure given the number of planets in the galaxy, as a matter of fact, one of Jupiter moons officially named "gamamede" is very much like earth in size and characteristics
Hunter
How to become an astronomy
Aakarsh Reply
astronomer*
Emilya
Yes
Aakarsh
Astronomer
Aakarsh
yes i Also want to know the answer
Mehar
How to become?
Aakarsh
Me too
Romancho
By hard study
Zulker
Try to keep all the basics of science subjects and also English
Zulker
Ya i know that I will do hard work but
Aakarsh
I have always found astronomy fascinating, but my first love is philosophy.
GARY
I wanna become astromer as neel armstrang
Aakarsh
that's an astronaut
Emilya
Neil Armstrong
antman
what is your name who are you where are you why are you there
GARY
Neil Armstrong was an astronaut. You first work is to know the meaning of astrophysicist, astronomer, astronaut, astrologer and to find the work of the individual. And the most important thing is to be good in English. Because u have done some mistakes while doing chat with me like :an astronomer
Zulker
sorry I'm talking to somebody else someplace else on the internet
GARY
The heading will be "How to become an astronomer"
Zulker
jus be yourself and follow your passion and I think there is no need to copy anyone
Aarushi
hey it's simple yaar, it's based on your curiosity
neehar
what is the length of Earth
comedy Reply
The Earth is not a perfect sphere, however it's roughly 25,000 miles, or 131.5 million feet, or 1.6 Billion inches. In the Metric system its HUGE!
Jocofranc
Thank for your knowledge.Sr
nyo
But can I also know and calculate the whole weight of earth includeing flora, funa,water on earth even air's weight.Depending on super compruter, I think it can be.For the very detail in the Metric System.Such as kilogram and pound.
nyo
Earth is about 6 Sextillion metric tons check out formula at ***science.howstuffworks.com/environmental/earth/geophysics/planet-earth-weigh.htm
Jocofranc
thank again Sr.I wanna ask another question if you don't mind.The earth had 4.5billion years age old.My question is from fire ball to today more and more stable geology was how happen.Please answer me starting of life on this planet and how many era are there and the earth history.
nyo
My friend you have asked a question(s) that scientists struggle with. There is no short cut...the information is lenghty. Here is an additional site for you. It is a good place to start. ***newscientist.com/article/dn17453-timeline-the-evolution-of-life/
Jocofranc
Sr,your web site is very useful to me.And another question is how gene or DNA transfer from parent to sibling.how we know the first DNA of our first human from arfarica.
nyo
Good morning Nyo; ur question is out of my league, although fascinating. Maybe you'll find this page helpful: ***genetics.thetech.org/ask/ask445
Jocofranc
If speed is so many thousand time of light and start to travel from one point,how speed will return to it starting point even in straight line back.Will time and energy be limit it?Can it be posible.Please let me explain Sr.
nyo
hey neo ur curiosity is great, where r u from?
neehar
in physics actully no but thory make possible
gdjm
earth is about 13,000 kilometers across
Hunter
there is aliens or parallel universe
Chithra Reply
There may be both who knows
Debabrata
It would be quite surprising to me to learn that there is no aliens in our very own galaxy. The size of our galaxy alone seems to favour life. There's so many reasons why we haven't made contact but as our technology grows we will undoubtedly find answers. I also think that it's possible that ...
Jocofranc
But I don't think that that alien species might be developed.... Because if they were developed or advanced than us then they must have located us first and might have even contacted us
Debabrata
many other universes exist. I don't think that they would be parallel universes in the purest sense of the word. Only speculations on my part. We simply dont know with certainty.
Jocofranc
Hi Debabrata; You may be right. It's hard to say with certainty. An ugly truth (guess really) is that Tellurian are simply not interesting. We are not all that!
Jocofranc
Yeah Jocofranc you are also right about parallel universe. Who knows what lies ahead.
Debabrata
the parallel universe theory is something secondary but first let's focus on the nearby objects like titan which shows great hope
Aarushi
I read it before about aliens, but I have to research on it
neehar
yeah of course
neehar
What about XTs... Exo-Tellurians. Ancient people who could have obtain a spurt of technology and left home. Progression of men r not always linear but sometime cyclic. Civilization comes and goes. Geo-upheaval can easily erase any evidence. Our bros r out there. (have fun 😁)
Jocofranc
sir jocofranc I think u didn't listen about aliens who send a message to our space research organization.
neehar

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Source:  OpenStax, Astronomy. OpenStax CNX. Apr 12, 2017 Download for free at http://cnx.org/content/col11992/1.13
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