Gravitation Physics 1425 Lecture 11

Gravitation: Modes of Reading in the Anthropocene
In this article, I suggest ‘gravitation’ as a new way of reading in and for the anthropocene, which is characterised by environmentally destructive ‘social acceleration’. This reading practice would imply two things: First, that representations of the natural environment take a primary position in relation to the characters in many genres, including those where nature so far has been read as a highly conventional construction. It also involves acknowledging that ultimately, characters are positioned by the physical environment in these genres, as characters, in one way or the other, can never exist unrelated to the environment that encompass and cut through them. These genres I suggest be called ‘gravitating genres’. Second, and in a similar fashion, I suggest the term ‘gravitating reading’ to denote reading of physical books, which in this context becomes a highly preferred medium. This term partly coincides with that of ‘deep reading’ suggested by Mangen, but in addition, it also recognizes the dependency of both the reader and the medium on the natural environment. Together, these two practices amount to, I suggest, nothing less than a mutually sustainable economy of reading.


So why doesn't the Earth go round the
Moon?
• The moon's mass is about 1% of the Earth's mass.• In fact, the Moon's attraction does cause the Earth to go in a circle-both Earth and Moon circle their common center of mass (which is inside the Earth!) We'll discuss this more later.
Gravitational Attraction is Proportional to Both Masses • We've already seen, from Galileo's observation of equal downward acceleration and Newton's Second Law, that the Earth attracts an object with a force proportional to the object's mass.• But from Newton's Third Law, the attractions are equal and opposite-symmetric.• Therefore, the attraction is also proportional to the Earth's mass.

Law of Universal Gravitation
• The story so far: • For two masses m 1 , m 2 at a distance r apart, the gravitational attraction between them is proportional to 1/r 2 • It is also proportional to both m 1 and m 2 .
• Therefore it must have the form where G is some constant.
Clicker Question: How could G be determined?Weighing the Earth • Cavendish called his experiment "weighing the Earth": he knew the inverse square law, the big balls had masses of about 150 kg, and were about 0.25 meters away from the small balls.• Comparing the attraction of the small balls to the big balls with the small balls' attraction to the Earth (the ratio was about 10 -8 ) and allowing for the different r's (ratio about 3x10 6 ) he found the mass of the Earth to be 6x10 24 kg, with about a 2% error from the known modern value.
Weighing the Sun… • Once we know G, we can find the mass of the Sun.
• Taking the Earth's orbit around the Sun to be a circle, the Sun's gravity providing the centripetal force, F = ma is simplifying to Putting in v = 30 km/sec , r = 150x10 6 km, G =6.7x10 -11 , we find M = 2x10 30 kg.
Weighing a Galaxy… • We can estimate the mass of a galaxy by measuring the centripetal acceleration of an outer star.We can also estimate it by just counting stars-but the mass turns out to be much greater that the total mass of visible stars.Most of the mass is dark matter. http://geology.com/nasa/nasa-universe-pictures.shtml Vector Form of Gravitational Force • The gravitational force is of course a vector, the attraction of sphere B on sphere A points from the center of A towards that of B, where is a unit vector pointing from A to B.
• The total force on A is

Massive Spherical Shell
• Imagine a massive hollow uniform spherical shell.• The gravitational force is the sum of the attractive forces from all parts of the shell.• Inside the shell, this force is zero everywhere!Smaller closer areas balance larger more distant areas.• Outside the shell, Newton proved the force was the same as if all the mass were at the center.
• A Clicker Question How will g change (if at all) on going from the Earth's surface to the bottom of a deep mine?
A. g will be a bit stronger at the bottom of the mine B. It will be weaker C. It will be the same as at the surface Clicker Answer How will g change (if at all) on going from the Earth's surface to the bottom of a deep mine?
It will be weaker!• Think of the Earth as built up of spherical shells, like an onion.Down the mine, you're inside the outermost shell, so it gives no net gravity.• If you're now r meters from the Earth's center, the remaining shells have volume r 3 /r earth 3 , but you're closer to the center so the 1/r 2 helps, but not enough: g is proportional to r.
• Think: what is gravity at the Earth's center?Kepler's First Law Each planet moves in an elliptical orbit with the Sun at one focus • He deduced this from analyzing many observations.• An ellipse is the set of points P such that PF 1 +PF 2 is constant, the points F 1 and F 2 are the foci, PF 1 means the distance from point P to point F 1 . • You can draw an ellipse by fixing the ends of a piece of string at A, B then, keeping the string tight, loop it around a pencil point at P and move the pencil around on paper.

About Ellipses…
• The standard notation is to label the two foci F 1 , F 2 .(The term "focus" is used because if a light is placed at F 1 , and the ellipse is a mirror, the reflected light all goes to F 2 .)• The eccentricity e of the ellipse is how far a focus is from the center C compared with the furthest point of the ellipse.• e = 0 means a circle: most planetary orbits are close to circles-for Earth, e = 0.017.
2b ea 2a is the length of the "major axis", 2b the length of the "minor axis" a is called the semimajor axis length.