Physics of AstronomyWinter Week 3 - Thus.

Half-hour closed-book quiz

Go over solutions together at 1:00

Midterm in class next Thus? Check syllabus

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Math-A: Universe Ch.3: Eclipses & Moon

Seminar

Math-B: Astrophysics Ch.2: Orbits

Week-3 quiz• Astronomy questions: Most of these are taken directly from the online quizzes. You should be able to answer them easily. If not,

move on to the next question.

• 1. Which of the following fundamental requirements must be met in order that a theory or idea can be considered a scientific theory? It has to explain all known observations.It has to be based upon mathematics.The theory should predict new observations, even if they prove the theory wrong.

• 2. What is a light year? Explain.A unit of time in astronomy: __________________________________A unit of angle in astronomy: __________________________________A unit of distance in astronomy: _________________________________

• 3. In a particular total solar eclipse, the Moon was observed from a location upon Earth to cover the Sun exactly, that is, the Moon's angular size was the same as that of the Sun at that time. If the Sun is 1.5 x 108 km away and has a diameter of 1.4 ´ 106 km, how far away is the Moon if its diameter is 3.5 x 103 km? 3.75 ´ 103 km3.75 ´ 105 km3.27 ´ 101km

• 4. The Earth is closest to the Sun during winter in the southern hemisphere.during summer in the southern hemisphere.when the Sun is directly overhead at the equator.

• 5. As the Moon orbits around the Earth, its path on the celestial sphere is very close to the celestial equator.is very close to the path followed by the Sun (the ecliptic).is very close to a line of right ascension, passing close to each celestial pole once each orbit.

• 6. The declination of the Sun on the first day of spring is variable, depending on the year.23.5º north.0º.

Week-3 quiz part 2Physics A question: Everyone should be able to answer this in about 10 minutes.1. (a) What is the fundamental relationship between force F and acceleration a?

_______(b) Do accelerations cause forces? Y N Or do forces cause accelerations? Y N

2. Write down the fundamental defining relationships between position, velocity, and acceleration. (Do not assume any of these variables are constant.)

(a) Differential relationships:v = a =

(b) Integral relationships: x = v =

3. Apply the appropriate relationships to find the position (x) and velocity (v) of a mass (m) which experiences a force F = mg – cv, where g and c are constants. Assume the initial position is x0 and the initial velocity is v0, at t=0.

Week-3 quiz part 3Physics B question: This is optional for A-group students. It should take

B-groups students about 10 minutes.

Consider a small mass (m) orbiting a big mass (M) with an orbit radius R and period T.

What is the centripetal acceleration a?

What is the force responsible for this acceleration?

Put these together to find a relationship between R and T, starting from F=ma.

Briefly describe what this means, in words.

Universe Ch.3

Moon survey:• What causes phases of the moon?• How much of the moon is lit at any given time? • Does the “dark side of the Moon” ever get sunlight?• Full moon rises at: New moon rises at:

noonSunset

MidnightDawn

• Lunar eclipse possible at: Solar eclipse possible at: Full moonNew moon

Universe Ch.3

Animations on Universe online

Each team pick a Ch.3 problem to try.

Sign up for presentations before you go, or in seminar.Give Thus. Seminar students first dibs on next Thus. Conference

times.

Astrophysics – C&O Ch.2

Kepler’s laws - review and application

Recall General form of K3

Simple form of K3 for solar system: For objects orbiting the Sun with a=radius in AU and p=period in years, a3=p2. (Why?)Ex: A satellite is placed in a circular orbit around the Sun, orbiting the Sun once every 10 months. How far is the satellite from the Sun? 2

3 2 10 a = p = _______12

a ______

Elliptical orbits

Make an ellipse: length of string between two foci is always r’ + r = 2a.

Eccentricity e = fraction of a from center to focus.

#2.1: Derive the equation for an ellipse.

Distance from each focus to any point P on ellipse:

r2=y2+(x-ae)2 r’2=y2+(x+ae)2

Combine with r+r’=2a and b2 = a2(1-e2) to get 2 2

2 2 1x ya b

#2.2: Find the area of an ellipse.

so y goes between

and x goes from (-a to +a)

Area =

22 2

21 xy ba

2

21 xy ba

2

2

2

2

1

1

xba a

x y a xba

dA dy dx dy dx

22 2 1Hint : sin ( 14.244)

2a xa x dx Schaum

a

Ch.2.2: Shell Theorem (p.36-38)The force exerted by a spherically symmetric shell acts as if its mass were located entirely at its center.

The force exerted by the ring of mass dMring on the point mass m is

Where s cos = r - R cos and s2 = (r - R cos )2 + (R sin )2 and

dMring = (R) dVring and

dVring = 2 R sin R d dR

2 cosringring

mdMdF G

s

Substitute this into dF and integrate

Change the variable to u = s2 = r 2 + R 2 - 2rR cos Solve for

cos

sin

Substitute these in and integrate over du to get

0

0

0

2

30 0

2

3/ 22 20 0

3

3/ 22 20 0

cos ( )2 sin

( ) sin22 cos

( ) sin cos22 cos

R

R

R

r R R RF Gm d dR

s

r R RGm d dRr R rR

R RGm d dRr R rR

02

20

4 ( )RGmF R R dR

r

Density = mass of shell / volume of shell

(R) = dMshell / dVshell

So dMshell =(R) dVshell = 4 R2 (R) dR

Which is the integrand of

So the force on m due to a spherically symmetric mass shell of dMshell:

The shell acts gravitationally as if its mass were located entirely at its center.. Finally, integrating over the mass shells, we find that the force exerted on m by an extended, spherically symmetric mass distribution is

F = GmM/r2

02

20

4 ( )RGmF R R dR

r

2shell shellGmdF dMr

Next week in Astrophysics Ch.2:

• Force and Angular momentum• Center of Mass reference frame• Virial Theorem

Problems from Ch.2: This week: 1, 2, 11Next week: 7, 8