Earth Orbit, Comets and Seasons

The Earth travels around the sun in an elliptical pattern, but it is still fairly close to a circular orbit.

The seasons on Earth are determined by the angle of sunlight that hits the planet according to the axis of rotation of the planet, not the proximity of the planet to the Sun.

A comet might heat up when closer to the Sun on an ellipse with a high eccentricity (deviation from perfect circle), but the Earth’s orbit does not have a high eccentricity.

Also, if you know part of an elliptical path you can figure out the period and axes of the ellipse.

It can thus be calculated that Halley’s comet actually does not go out as far from the Sun as Pluto.

Gravity Potential Energy in Space

In space there is potential energy that is gravitational, similar in some ways to the potential energy associated with height on earth, but also different.

Two objects must be present and the potential energy increases with less distance between them, instead of more height like on earth.

The potential energy will be at a maximum absolute value when the radius between is smallest, but it is considered negative since the objects are moving toward each other.

They will also have the most kinetic energy right before they collide rather than zero kinetic energy when an object on earth hits the ground.

Gravity Drilling to the Center of the Earth

If you were to drill a hole through the center of the earth the result might seem a little counter intuitive.

Gravity decreases with distance, away from the earth, ie in outer space, and it also decreases as you travel toward the center of the earth.

The reason is that the force of gravity on an object will only come from the inner layers (relative to position of the object).

The volume of the sphere with radius of the distance from the center will affect you, not any outside layers, since the outside layers will cancel forces.

The part of the outside layer near to you will be closer with less mass and the part farther away will have more mass (proportional inversely to square of distance).

Changing Coordinate Systems to Make Problems Easier

One day a physicist comes across a perplexed student in the library.

It seems that the student had only learned to place his axes with the positive y axis going up and the positive x axis going to the right.

Unfortunately this system wasn’t working so well with a situation involving pulleys and curved directions.

The physicist decides to help the engineer by telling him that the x-y coordinate system can be changed to better suit the problem at hand, much like polar coordinates can be more convenient than cartesian coordinates.

If an object travels in a curved path he reasons that the x-y coordinate system may also be curved in parts for simplicity.

Gravity may be thought of as positive or negative and up may be considered down.

The physicist also says that simply using common sense to check an answer will often times be effective, for instance if a block is sitting on a wall with no forces it will probably just stay there.

Falling Velocity – Breaking a Container

Late one night a group of physics students dressed all in black and equipped with night vision sneak into Kesten’s office and steal a metal container labeled “Chug’s Secrets.”

They learned the a2 = (a+b)(a-b)+b2 rule for squaring numbers and thought that they might learn amazing tricks for mastering physics by seeing how Chug worked his magic.

By using THE TRUTH these students calculated that they could break the metal container by dropping it from the top of (four story) Casa Italiana, but unfortunately they didn’t look at the situation carefully and in their calculations placed y0 at ground level and had a positive acceleration for gravity.

The final velocity was not sufficient and the container did not break, luckily a former student of Kesten heard the clang of the metal and helped the students understand their computational errors and also advising them to go to 11 story Swig.

At Swig the group had a baseball player throw the container as fast as he could down at the ground, since a higher v0 in the right direction will produce a higher velocity.

The container broke on impact!

Unfortunately the final velocity was so strong that the police heard the noise and took the container to Area 51, since then “Chug’s Secrets” have still not been uncovered.