# Exam Two Info

### Contents of the Exam

The Second Exam will cover material presented in the lectures since exam 1. In the text this is from page 33 (Galileo) to page 52 (excluding the topics of "Angular Momentum" on page 47 and "Orbital motion and Mass" on page 49. From my "ASTR 121 Course Outline", the topics go from "Planetary Configurations" to "Bound and Unbound Orbits", excluding conservation of angular momentum and Newtons version of Kepler's 3rd law.

### Format of the Exam

The Exams for this course are true/false, multiple choice and short answer format. The review questions at the end of the chapters are typical, including the advanced questions. Below I supply a few sample questions so you know what to expect. Note: this sample is not comprehensive, it is approximately representative although it emphasises questions with a bit more math, since these are the kind of questions which most people have the most trouble with.

### Sample Questions

1. You are on Mars. It is martian midnight. You see a planet high in the sky. Which of the following planets could that planet be?

1. Earth
2. Venus
3. Saturn
4. Any of the above

2. T/F A new inferior planet is discovered, and found to have a greatest elongation of 14.5 degrees. Assuming it has a circular orbit, its distance from the Sun is 0.25 AU

3. Retrograde motion of Mars occurs near the time when:

1. Mars is in conjunction
2. Mars in in Quadrature
3. Mars is at greatest elongation
4. Mars is in opposition

4. The Synodic period of a planet is the interval of time between :

1. one quadrature and the next quadrature
2. opposition to the next opposition
3. superior conjunction to the next superior conjunction
4. eastern quadrature to the next eastern quadrature
5. passing into Virgo (as seen from the Sun) and the next passing into Virgo (as seen from the sun)
6. a, b and c
7. b, c and d
8. b, c, and e

5. Describe a telescopic discovery of Galileo and state what idea of Ptolemy and Aristotle that the discovery disagreed with.

6. How did Tycho Brahe's observations of a new star in Cassiopeia undermine standard Aristotelian teaching.

7. Sketch an elliptical orbit, and label the position of the Sun, perihelion, aphelion, the major and minor axes, and estimate its eccentricity.

8. State Kepler's 2nd law. From this, at which point in its orbit does a planet (a) move fastest, and (b) move slowest.

9. [A difficult extension of the last question. Hint : use Kepler's 2nd law]. A planet moving on an ellipse of eccentricity 0.5 travels at a speed of 10 km/s at aphelion. What its its speed at perihelion?

1. 10 km/s
2. 1/3 km/s
3. 30 km/s
4. 90 km/s
5. not enough information is given

10.An asteroid moves in a circular orbit about the Sun. If the orbital period is 8 years, what is its distance from the Sun?

1. 8 AU
2. 64 AU
3. 4 AU
4. 2 AU
5. 16 AU

11.What is the difference between speed and velocity as scientifically defined?

1. The two terms mean essentially the same thing.
2. An object's velocity is always greater than its speed.
3. A statement of velocity includes direction; speed doesn't.
4. An object's velocity is always less than its speed.

12. If the same force is applied to two objects, object A with a mass of 1 kilogram, and object B with a mass of 2 kilograms, which of the following statements will be true?

1. Object A has twice the acceleration of object B
2. Object B has twice the acceleration of object A
3. Object A and object B have the same acceleration
4. Object B has four times the acceleration of A

13. Consider two equal-massed objects separated by 10 meters. If that distance is halved to 5 meters, the attractive force of gravity between them will

1. be halved.
2. remain the same.
3. be doubled.
4. be increased four times.
5. be decreased four times.

14. If the sun were to suddenly vanish, what would the motion of the earth become (ignore the presence of the moon) ?

1. with no force acting, it would stand still
2. it will move directly away from where the sun once stood, in response to the last presence of centrifugal force
3. it would spiral outwards
4. it would settle into a larger orbit.
5. it would continue to move in a straight line with the same velocity it had the instant the sun vanished

15. T/F Scientifically speaking, "Weightloss programs" should more properly be called "Massloss programs"

16. On earth, the acceleration due to gravity, gE is 10 m/s/s. Planet A has the same size as the earth but is twice as massive. What is the acceleration due to gravity on planet A ? Lets continue. Planet B has the same mass as planet A but has twice its size (ie radius). What now is the acceleration due to gravity on planet B ?

17. T/F When in orbit about the earth, the space shuttle must keep one of its rocket engines going to prevent it falling back to earth.

18. T/F If an object is moving on a hyperbolic orbit, it will never return.

Do the 18 questions, write down your choice of answers, then check yourself with these Answers Think about the ones you missed. If you missed several, redouble your study efforts ! Also, dont forget the TA office hours in room 267 of 9am - noon (Tues, Thurs) and 3:30pm - 6:30pm (Mon, Wed, Fri). And my own office hours 2pm to 3pm (Mon, Wed, Fri).

Below are listed the main themes covered in class, some posed as questions.

A. Starting with the Copernican model, understand how this explains retrograde motion.

B. Know what it means to talk about "Planetary Configurations" and how these refer to the position of a planet in the sky relative to the sun. Know the terms Superior and Inferior planets, opposition, quadrature, conjunction, greatest elongation. Know what planetary phase goes with what configuration. Know how to calculate the orbit size for an inferior planet using its greatest elongation.

C. Know what Synodic and Siderial periods are. Which is the more astrophysically important? Siderial periods can be determined from synodic periods and the length of our year (but you do NOT need to know how to do this).

D. Using the newly discovered telescope, what important observations did Galileo make which cast doubt on the Aristotle's teaching? Know, roughly, Galileo's dealings with the Catholic church during this time.

E. Know about Tycho Brahe's contributions to the unfolding story : principally a huge high quality dataset of planetary positions spanning 20 yrs, with typical accuracy of about 1 minute of arc. Also know about his discovery of a supernova, and the observations he made which went against the Aristotle's teachings (undetectable parallax suggesting it was beyond the moon). Why did he adopt a model which was a hybrid of the Copernican and the Ptolemeic models. Know, roughly, a little of his history and how Kepler came to get his data.

F. Know Kepler's thee laws of planetary motion. Be able to label an ellipse, including perihelion, aphelion, focus, major axis, eccentricity. Be able to define and evaluate eccentricity, and --- realise that planetary orbits are very close to circles. What is a typical planetary eccentricity. Understand how Kepler's 2nd law describes how a planet changes speed around its orbit. Understand how to apply Kepler's 3rd law in simple examples : eg for planets orbiting the sun, or for moons orbiting other planets.

G. Be basically familiar with the evolution of our understanding of motion and forces : Aristotle up to Galileo and finally Newton. Know Galileo's experiments : by removing friction, objects naturally continue to move; objects accelerate when they fall; heavy and light objects fall "together".

H. Know the difference between Scalars and Vectors. Know some examples of each (Mass, Temperature, Speed, Length, Volume are all scalars, while Velocity, Acceleration, Force, Momentum, Weight are all Vectors). Understand that acceleration of an object is the CHANGE in velocity occuring in one second, and so has units of m/s/s (in a certain direction).

I. Know well, Newton's three laws of motion and one law of gravitation. 1st : with no net force acting, an object maintains constant velocity (which could be stationary). 2nd : With a net force acting, an object accelerates parallel to the force with magnitude equal to Force/Mass. (this is equivalent to F = m x a). 3rd : When one object applies a force on another, the second object pushes back with an equal and opposite force. Gravity : two masses attract eachother with a force Fgrav = G x M1 x M2 / R2, where M1 and M2 are the two object masses, and R is their separation. G is Newton's gravitational constant which is very small in the mks system of units (but you dont need to know the value of the constant).

J. Know some examples of each of these Laws. 1st : rolling ball on horizontal surface; people coasting on an ice rink. 2nd : acceleration of a car --- use the gas pedal, use the break, use the stearing wheel. Stearing wheel causes road friction to push the car around a corner, the acceleration is perpendicular to the curve, as is the force. Pushing a car or a bicycle --- the lighter accelerates faster. 3rd : two people on ice rink push eachother, lighter goes off faster, even if they "do the pushing". Gravity : pulls on an apple, causing it to accelerate when it falls. Deflects passing asteroids. Gets weaker for greater separation between the objects. Realise, also, that for spherical objects (eg planets and stars) the gravitational pull from the entire planet is exactly same as if all the mass of the planet were at the center of the sphere.

K. Understand the difference between Weight (gravitational force, so vector) and Mass (intrinsic to the object, and a scalar). Weight is the total gravitational force acting on an object, with units of Newtons (in mks system) or lbs (english system). Your weight is context dependent, differing from one planet to the next, while your mass is fixed and independent of where you are (and has units of Kg, in mks system).

L. On earth's surface, Weight of m is Fgrav = G ME x m / (RE)2 where ME is the Earth's mass and RE is the Earth's radius. This weight force will yield an acceleration : the "acceleration due to gravity", written "g" for the earth. So Fgrav = G ME x m / (RE)2 = m x g. Hence, since m is on both sides we have for acceleration of falling objects : g = G ME / (RE)2 = 9.8 m/s/s (in mks) or 32 ft/s/s (in english unts). Note that g is independent of the objects mass, hence "light and heavy objects fall at the same rate" (Galileo's observation). Also, the acceleration due to gravity is different on other planets because they have different Masses and Radii.

M. Understand basic circular motion (eg mass on end of string) --- a force acts since motion is not straight and constant, this is the centrepetal force. The reaction force on the central object pulling out is the centrifugal force. If gravity gives the force, then the circular motion is an "orbit". In more detail : the object's motion has two parts, a tangential component which would be the velocity in the absence of the central pull, and a radial velocity (falling) resulting from the gravitational pull. The sum of these velocities gives a actual velocity which is along the line of the orbit. Objects in orbit are therefore continually "falling" downwards to the center, never hitting it because they are also going sideways so they "constantly miss" the central object.

N. Know Newton's diagram of a canon shooting a ball with ever faster horizontal speed, until finally, as it falls, the earth's surface curves away at the same rate, and the object never strikes the ground --- it is truely in orbit. In these orbits the objects are continually in "free fall" --- only gravity is acting.

O. Newton was able to show (using calculus) that with faster or slower canon balls (and ignoring collisions with the earth's surface) the orbital shapes could be any of the "conic sections" : circle, ellipse, parabola, and hyperbola. Circular or elliptical orbits are clearly periodic and therefore "bound" to the earth (or sun), with the moon and planets providing good examples of this type of orbit. Hyperbolic orbits are open and an object will never return, going out to "infinity" and continuing to coast along even out there --- "unbound" from the earth (or sun). Passing stars are on hyperbolic orbits. Finally, one conic section lives just at the boundary between bound and unbound orbits, it is the "marginally bound" orbit, the parabola, which goes way out and barely turns around. This type of orbit is found for a number of "long period comets".