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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 .

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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

general equation for photosynthesis
Ojasope Reply
6CO2 + 6H2O + solar energy= C6H1206+ 6O2
Anastasiya
meaning of amino Acids
AJAYI Reply
a diagram of an adult mosquito
mubarak Reply
what are white blood cells
Mlungisi Reply
white blood cell is part of the immune system. that help fight the infection.
MG
what about tissue celss
Mlungisi
Cells with a similar function, form a tissue. For example the nervous tissue is composed by cells:neurons and glia cells. Muscle tissue, is composed by different cells.
Anastasiya
I need further explanation coz celewi anything guys,,,
Calvin Reply
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on what?
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Lish
is air homogenous or hetrogenous
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homogenous
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Isala
explain if oxygen is necessary for photosynthesis
Allice Reply
explain if oxygen is necessary for photosynthesis
Allice Reply
Yes, the plant does need oxygen. The plant uses oxygen, water, light, and produced food. The plant use process called photosynthesis.
MG
By using the energy of sunlight, plants convert carbon dioxide and water into carbohydrates and oxygen by photosynthesis. This happens during the day and sunlight is needed.
NOBLE
no. it s a product of the process
Anastasiya
yet still is it needed?
NOBLE
no. The reaction is: 6CO2+6H20+ solar energy =C6H12O6(glucose)+602. The plant requires Carbon dioxyde, light, and water Only, and produces glucose and oxygen( which is a waste).
Anastasiya
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NOBLE Reply
joining
Godfrey
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NOBLE
the study of non and living organism is called.
Godfrey
Is call biology
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NOBLE
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what Is ecology
Musonda Reply
what is a cell
Emmanuel Reply
A cell is a basic structure and functional unit of life
Ndongya
what is biolgy
Hawwi Reply
is the study of living and non living organisms
Ahmed
may u draw the female organ
MARTIN Reply
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DAVID
anabolism and catabolism
Sani Reply
Anabolism refers to the process in methabolism in which complex molecules are formed "built" and requires energy to happen. Catabolism is the opposite process: complex molecules are deconstructed releasing energy, such as during glicolysis.
Anastasiya
Explain briefly independent assortment gene .
Otu Reply
hi
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hi I'm Anatalia
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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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