Astronomy 105G Lecture Notes, 28 Jan. 2004

Announcements

• Reading: Ch. 2 pp. 52-56
• Special KRWG-TV event about astronomy on Saturday Jan. 31 - EXTRA CREDIT
• Quiz 1 on Mon. Feb. 2
• Labs next week will meet at the football field in Aggie Memorial Stadium. Park across the street on the north side, in the Pan American Center parking lot.

Last Time:

• Kepler's Laws
• Newton's Law of Gravitation
• Mass, Volume, and Density

Today:

• Newton's Law of Gravitation (more)
• Orbits and Gravity
• Seasons

Newton's Laws of Gravitation

Newton's Law of Gravitation is given by the following equation:


F_g = G [(M₁ M₂)/(R²)], where


G is called the gravitational constant
M₁ is the mass of object 1
M₂ is the mass of object 2
R is the distance between objects 1 and 2

The most important things to remember about gravity are the following:

• Every object is attracted to every other object through gravity - that is why this law is known as Newton's Universal Law of Gravitation.


• The gravitational force is directly proportional to the mass: the larger the mass, the larger the force; the smaller the mass, the smaller the force. So if we double the mass of one of the objects, the Gravitational Force also doubles.


• The force is inversely related to the distance: the larger the distance, the SMALLER the force; the smaller the distance, the LARGER the force. So if we double the distance between objects 1 and 2, the gravitational force will decrease by a factor of 2², or 4.

Mass vs. Weight

We said previously that an object's Mass is the amount of material (atoms, molecules, etc.) it contains. Your mass does not change as you move from Earth to the Moon, for example (unless you ate 12 boxes of doughnuts along the way!).

An object's weight is a measure of the gravitational force felt by the object. Thus, it depends not only on your mass, but on the mass of the objeect you're standing on. If you travel to the Moon, you will weigh less there because the gravitational force it exerts on you is smaller (about one sixth of what you feel on Earth).

What about the Mars Rovers, that landed on Mars in a protective envelope of airbags? Is the gravity they are experiencing stronger or weaker than what they would have felt on the surface of the Earth? For comparison, the radius of Mars is approximately one-half the radius of the Earth, and the mass of Mars is roughly one-tenth the mass of the Earth.

Images from http://marsrovers.jpl.nasa.gov/gallery/images.html

Orbits and Gravity

If you throw a baseball, gravity will pull it back to Earth.

If you throw it even harder, it will go farther but still fall back to Earth.

If you could throw it with an extremely high velocity, it would travel completely around the Earth, always falling in the gravitational field but never reaching the Earth, which is curving away at the same rate that the baseball falls. That is, the baseball would have been put into orbit around the Earth.

Newton concluded that the orbit of the Moon was of exactly the same nature: the Moon continuously "fell" in its path around the Earth because of the acceleration due to gravity, thus producing its orbit.

Graphics courtesy of http://csep10.phys.utk.edu/astr161/lect/history/newtongrav.html.

Seasons

One of the most common misconceptions about astronomy is the cause of the seasons on Earth. The seasons are NOT due to the fact that the Earth is closer to the Sun in June and farther from the Sun in January! In fact,

• The Earth's orbit is so close to being circular that the perihelion vs. aphelion distances are nearly the same
• The Earth's perihelion occurs in January!!

The seasons on Earth are due to the fact that the Earth's rotation axis is tilted 23 degrees relative to a line perpendicular to the plane of its orbit.

In June, the northern hemisphere of the Earth is "leaning towards" the Sun. At that time, the northern hemisphere receives more direct sunlight, and for a longer amount of time each day. In January, the northern hemisphere of the Earth is "leaning away" from the Sun (and the southern hemisphere is leaning towards the Sun).

Thought question: Mars' axial tilt is 25.2 degrees. Would you expect the seasons on Mars to be more or less extreme than they are on Earth? What about for Merucry, which has no axial tilt (0 degrees)?