Planet "lab"

Lab 4 - Tour of the Planets

Please determine many interesting tidbits of trivia about our solar neighbors. You may like the following website:

http://nineplanets.org/

Please answer the following questions, based on your reading and web discovery. Some questions might have several answers, while the answer to others might be "none of them."

Which planet(s):

1. Rotates backwards?
2. Revolves backwards?
3. Rotates nearly on its side?
4. Have more than 10 moons?
5. Have only one moon?
6. Has an orbit with the greatest inclination to the ecliptic?
7. Is the furthest planet known to the ancients?
8. Has a largely methane atmosphere?
9. Has a nondescript, pale greenish color?
10. Has a blemish known as the great dark spot?
11. Has a fine iron oxide regolith?
12. Is most similar to Earth in its surface gravity?
13. Has the greatest mass?
14. Has the smallest diameter?
15. Have been visited by humans?
16. Has the strongest magnetic field?
17. Has rings?
18. Has sulfuric acid clouds?
19. Has the tallest mountain in the Solar System (and what is it)?
20. Has a day longer than its year?
21. Has been landed on most recently by spacecraft?
22. Experiences global dust storms?
23. Has a moon that rotates retrograde (and what is it)?
24. May be an escaped Kuiper object?
25. Was once thought to be a failed star?
26. Is heavily cratered?
27. Has moons which are likely candidates for life?
28. Was hit by a large comet in the last several years?
29. Is most oblate?
30. Has a central pressure 100 million times Earth's atmospheric pressure?

Now for the minor bodies.

1. Which body is an asteroid with its own orbiting asteroid?
2. Which moon has erupting volcanoes?
3. Which body is the largest asteroid?
4. Approximately how many known asteroids are there?
5. Approximately how many known Kuiper objects are there? What is the Kuiper belt?
6. How large is the Oort Cloud? What is the Oort Cloud?
7. Which moon was the first discovered after the Galilean satellites?

solar storm fyi

http://news.yahoo.com/biggest-solar-storm-years-bombarding-earth-now-064402504.html

http://www.spaceweather.com/

Quiz lab etc

Don't forget

Constellation / sky quiz on Friday.

Kepler lab due

Notes on space

Coordinate systems:

On Earth:

Longitude

half-circle lines from North to South pole
Zero longitude runs through the site of the Royal Greenwich Observatory in England - the Prime Meridian (0 degrees long.)
Number of degrees east or west of the PM

Latitude

Full circle lines parallel to the equator (0 degrees latitude)
+ or - 90 degrees corresponds to the poles

International Date Line (IDL)

Near or along 180 degrees longitude line, through the Pacific Ocean
As we travel eastward around the globe, the hours get later roughly each 15 degrees (a time zone). When we cross the IDL, we go BACK one day. This keeps only 24 hours on the Earth at a time.


In the Sky:

Celestial Equator

imaginary line above the Earth's equator

Right Ascension (RA)

Celestial analog of longitude (both measure east-west)

Measured in hours (each hour of RA equals 15 degrees) along the celestial equator

Declination (dec)

Celestial analog of latitude (both measure north-south)

Measured perpendicularly above (+) or below (-) the celestial equator

RA and dec form a coordinate system fixed to the stars. To observers on Earth, the stars appear to revolve every 23 h 56 min. So, the coordinate system appears to revolve at the same rate. Of course, it is the Earth which is really moving (most noticeably).

Ecliptic

Although the stars are fixed in their positions in the sky, the Sun's position varies through the whole range of RA throughout the year. This path (the "apparent" path of the Sun) is called the ecliptic and is inclined 23.5 degrees with respect to the celestial equator (CE), since the Earth's axis is tipped by that amount. (The "ecliptic plane" is the plane that the Earth and Sun make.)

The ecliptic and CE cross at two points:

Vernal equinox

March 21 (approx)

the first day of Northern Hemisphere spring

the zero-point of RA

Sun's declination is 0 degrees

Nearly equal amounts of day and night

Autumnal equinox

Sep 23 (approx)

the first day of autumn

Sun's declination at 0 degrees

Nearly equal amounts of day and night

Two other noteworthy days:

Winter solstice

Dec 22 (approx)

Shortest day of the year in Northern hemisphere

9.5 h of daylight (in the DC area)

As you travel farther north, the days are even shorter

- in Anchorage, Alaska, the day will be 5 h long

- in Barrow, Alaska, the sun will not "come out" at all; noontime is like deep twilight

the North pole is angled most steeply away from the Sun

Summer solstice

June 21 (approx)

longest day of the year in the Northern hemisphere

amount of tipping toward Sun is greatest for N. hemisphere

Sun highest in sky (dec is 23.5 degrees)

Length of daylight depends on latitude, calendar date, but not longitude

Each point on the globe receives an average of 12 hours of light each day. So, students in Barrow, Alaska have several days of endless sunshine as well.

Since the Moon goes around the Earth, its RA changes through the entire range of values each month. Since its orbit is inclined to the CE, its dec also changes.

A discussion on Time

The second is the fundamental unit of time. It was originally defined as:

- the amount of time required for a 1-m pendulum to swing from one side of arc to the other

Now, it is defined as:

9 192 631 770 cycles of radiation corresponding to the transition between two hyperfine levels in the ground state of Cesium-133

Worth noting:

There are approx 365 1/4 mean solar days in one solar year (watch time). The mean solar day is the average length of a solar day, 24 hours.

Solar year - the time between 2 vernal equinoxes. This is actually the tropical year, which is growing shorter by 0.5 sec/century. 19000 is the standard tropical year.

Sidereal time - time by the stars

Sidereal year - the amount of time for the Sun to return to a given position among stars

Calendars:

Julian - 365 days with an extra day every 4 years (leap year)

This was still a bit imprecise - consider that in 1988, the year was 365 d, 5 h, 48 min, 43.5 s.

By 1582, the Julian calendar was out of phase with Easter by nearly 10 days. So, Pope Gregory XIII adopted a new calendar; 10 days were dropped from that year.

Gregorian calendar -

Years evenly divible by 4 are leap years. Every 4th century year is a leap year (2000, 2400; NOT 1600, 1700, 1800, 1900, 2100)

Daylight savings time

Changed a few years back. Now:

Starts at 2 AM, second Sunday in March - set clocks AHEAD 1 hour

Ends at 2 AM, second Sunday in November - set clocks back

We are EST, Eastern Standard Time. During DST, we become EDT (Eastern daylight time).

GMT

Greenwich Mean Time; 5 hours ahead of EST. Roughly the same as Universal Time (UT).

UT

Universal time

Basically the mean solar time as measured on the Greenwich meridian, thus, 5 hours ahead of us.

Formally, UT is defined by a mathematical formula as a function of sidereal time and is thus determined by observations of stars.

Sidereal time

In 365 1/4 solar days, Earth makes 366 1/4 rotations on its own axis. So, there are 366 1/4 sidereal days in a solar year. Each sidereal day is shorter by about 4 minutes than a solar day. UT and GST agree at one instant every year (at the autumnal equinox, around Sep 22). Thereafter, the difference between them grows, in the sense that ST runs faster than UT until exactly half a year later, when it is 12 hours. Another half-year later, the times again agree.

Local Sidereal Time

the hour angle of the first point of Aries

Greenwich Sidereal Time

local sidereal time on the Greenwich meridian

Julian Date (JD)

Jan 1, 4713 BC is the fundamental epoch from which this is decided. The Julian date is the number of days since this day.

There is no year 0 in astronomy. The year before 1 AD is defined as year 0. So, 10 BC is the year -9 in astronomy.

That trick again: to go from BC year to astro year, subtract one and change sign.

Newton and Kepler

Newton's take on this was quite different. For him, Kepler's laws were a manifestation of the bigger "truth" of universal gravitation. That is:

All bodies have gravity unto them. Not just the Earth and Sun and planets, but ALL bodies (including YOU). Of course, the gravity for all of these is not equal. Far from it. The force of gravity can be summarized in an equation:

F = G m1 m2 / d^2

or.... the force of gravitation is equal to a constant ("big G") times the product of the masses, divided by the distance between them (between their centers, to be precise) squared.

Big G = 6.67 x 10^-11, which is a tiny number - therefore, you need BIG masses to see appreciable gravitational forces.

This is an INVERSE SQUARE law, meaning that:

- if the distance between the bodies is doubled, the force becomes 1/4 of its original value
- if the distance is tripled, the force becomes 1/9 the original amount
- etc.

Weight

Weight is a result of local gravitation. Since F = G m1 m2 / d^2, and the force of gravity (weight) is equal to m g, we can come up with a simple expression for local gravity (g):

g = G m(planet) / d^2

Likewise, this is an inverse square law. The further you are from the surface of the Earth, the weaker the gravitational acceleration. With normal altitudes, the value for g goes down only slightly, but it's enough for the air to become thinner (and for you to notice it immediately!).

Note that d is the distance from the CENTER of the Earth - this is the Earth's radius, if you're standing on the surface.

If you were above the surface of the earth an amount equal to the radius of the Earth, thereby doubling your distance from the center of the Earth, the value of g would be 1/4 of 9.8 m/s/s. If you were 2 Earth radii above the surface, the value of g would be 1/9 of 9.8 m/s/s.

The value of g also depends on the mass of the planet. The Moon is 1/4 the diameter of the Earth and about 1/81 its mass. You can check this but, this gives the Moon a g value of around 1.7 m/s/s. For Jupiter, it's around 2.5 m/s/s.

Kepler's Laws

Kepler and Newton
First, the applets:

http://www.physics.sjsu.edu/tomley/kepler.html

http://www.physics.sjsu.edu/tomley/Kepler12.html
for Kepler's laws, primarily the 2nd law

http://www.astro.utoronto.ca/~zhu/ast210/geocentric.html
for our discussion on geocentrism and how retrograde motion appears within this conceptual framework

Cool:
http://galileo.phys.virginia.edu/classes/109N/more_stuff/flashlets/kepler6.htm

http://physics.unl.edu/~klee/applets/moonphase/moonphase.html

>

Now, the notes.

Johannes Kepler, 1571-1630

Kepler's laws of planetary motion - of course, these apply equally well to all orbiting bodies

1. Planets take elliptical orbits, with the Sun at one focus. (If we were talking about satellites, the central gravitating body, such as the Earth, would be at one focus.) Nothing is at the other focus. Recall that a circle is the special case of the ellipse, wherein the two focal points are coincident. Some bodies, such as the Moon, take nearly circular orbits - that is, the eccentricity is very small.

2. The Area Law. Planets "sweep out" equal areas in equal times. See the applets for pictorial clarification. This means that in any 30 day period, a planet will sweep out a sector of space - the area of this sector is the same, regardless of the 30 day period. A major result of this is that the planet travels fastest when near the Sun.

3. The Harmonic Law. Consider the semi-major axis of a planet's orbit around the Sun - that's half the longest diameter of its orbit. This distance (a) is proportional to the amount of time to go around the Sun in a very peculiar fashion:

a^3 = T^2

That is to say, the semi-major axis CUBED (to the third power) is equal to the period (time) SQUARED. This assumes that we choose convenient units:

- the unit of a is the Astronomical Unit (AU), equal to the semi-major axis of Earth's orbit (approximately the average distance between Earth and Sun). This is around 150 million km or around 93 million miles

- the unit of time is the (Earth) year

e.g. Consider an asteroid with a semi-major axis of orbit of 4 AU. We can quickly calculate that its period of orbit is 8 years (since 4 cubed equals 8 squared).

Likewise for Pluto: a = 40 AU. T works out to be around 250 years.