Question

The stars, gas and dust in a galaxy rotate about the center of the galaxy. We would like to know exactly how to describe the rotation of all parts of the galaxy. In other words, we want to know if galaxies rotate like merry-go-rounds, or like planets orbit the Sun, or in some other way.

1. Do points near the center of a merry-go-round complete a full rotation in the same amount of time as points near the outer edge of the merry-go-round?

2. How does the distance traveled by a point near the center of a merry-go-round compare to the distance traveled by a point near the outer edge of the merry-go-round when they complete a full rotation?

3. Imagine you are on a rotating merry-go-round. Describe how your speed would change as you moved from standing at the center of a merry-go-round to the outer edge.

We know that the planets in our solar system all orbit the Sun. Furthermore, we know that the planets are all located at different distances from the Sun and from Kepler's 3rd Law we know that the planets have different orbital periods depending on their distances from the Sun.

4. How does the distance that a planet near the Sun travels in one complete orbit compare to the distance traveled in one complete orbit by a planet that is located far from the Sun?

If the planets all orbited the Sun with the same speed, then a planet located two times farther than Earth's distance from the Sun would have an orbital period exactly two times longer than Earth's orbital period.

5. The Earth orbits the Sun at a distance of 1 AU and takes 1 year to complete its orbit. Jupiter orbits the Sun at a distance of 5.2 AU and takes 11.9 years to complete its orbit. Which of these two planets orbits the Sun with the faster speed and which has the slower speed?

6. For our solar system, how do the speeds of the planets change as you move away from the Sun?

this is all the information that was given on my worksheet.

Answer #1

1) the points near the center of merry go round complete the full rotation in same time as compared to time taken by point near the outer edge. It is so because all the points in the system have same angular velocity.

2) the distance moved by point near the center of merry go round in one complete rotation is less than the distance moved by point near the outer edge , because circumference of outer edge is greater than the circumference of point near the center of merry go round.

3) as we move from center of merry go round , towards the outer edge , the moment of inertia increases and hence the angular velocity decreases because the angular momentum is to remain constant (angular momentum = moment of inertia× angular velocity).

As seen in class we can map out the orbits of stars near the
very center of our Galaxy. Star S2 orbits in 15.2 years, with an
orbit size of 840 AU. How much mass is there at the center to
explain this orbit?

The planet Mercury has an orbital period of 87.97 days, and its
greatest distance (aphelion distance) from the Sun is 0.4667 AU
{where 1 AU " 1 Astronomical Unit = 1.496x1011 m}. The mass of the
planet Mercury is 3.302x1023 kg and the mass of the Sun is
1.988x1030 kg. (a) Calculate the eccentricity of planet Mercury’s
orbit around the Sun. ! (b) Calculate the highest speed of planet
Mercury as it orbits around the Sun?

Given that the Sun moves in a circular orbit of radius 8.09 kpc
around the center of the Milky Way, and its orbital speed is 216
km/sec, work out how long it takes the Sun to complete one orbit of
the Galaxy. How many orbits has the Sun completed in the 4.5
billion years since it formed?
____ × 108 years
_____ orbits

The U.S.S. Enterprise (NCC‑1701) approaches an unknown system with
a Black Hole at the center. One of the planets in this system is
observed to have an orbit with a radius of R1 = 2.6 AU
and a period of T1 = 0.4 years. What is the mass of the
Black Hole compared to the mass of the Sun?
The mass 109.81 solar mass
Another planet in the system is observed to have an
orbital radius of R2 = 6.6...

Astronomers have observed a small, massive object at the center
of our Milky Way galaxy. A ring of material orbits this massive
object; the ring has a diameter of about 10 light years and an
orbital speed of about 110 km/s .
a) Determine the mass of the massive object at the center of the
Milky Way galaxy. Give your answer in kilograms.
b) Give your answer in solar masses (one solar mass is the mass
of the sun).
c)...

The planet Gliese 163 c, discovered in 2012, is a potentially
habitable world which is approxi- mately 7 times same mass as the
Earth, orbiting a small red dwarf star that is only 0.4 times mass
of the Sun. Completing its entire orbit in only a little over 25
days, Gliese 163 c orbits at a distance from its star at a speed of
1.78 times that of the speed of the Earth around the Sun.
Approximating that both the...

The figure shows an overhead view of a ring that can rotate
about its center like a merry-go-round. Its outer radius
R2 is 1.0 m, its inner radius
R1 is R2/2, its mass
M is 7.9 kg, and the mass of the crossbars at its center
is negligible. It initially rotates at an angular speed of 7.3
rad/s with a cat of mass m = M/4 on its outer edge, at
radius R2. By how much does the cat increase...

The figure shows an overhead view of a ring that can rotate
about its center like a merry-go-round. Its outer radius R2 is 0.9
m, its inner radius R1 is R2/2, its mass M is 8.0 kg, and the mass
of the crossbars at its center is negligible. It initially rotates
at an angular speed of 8.5 rad/s with a cat of mass m = M/4 on its
outer edge, at radius R2. By how much does the cat increase...

We know that most of the mass (>99%) of the solar
system is in the Sun. Is this consistent with the masses you
calculated in the first table, and the solar system rotation curve?
Explain your answer.
Planet
Distance from Sun (AU)
Orbital Velocity (km/s)
Mass inside orbit = v2r/887
(solar masses)
Mercury
0.4
47.4
1.013195
Venus
0.7
35.0
0.966741
Earth
1.0
29.8
1.001172
Mars
1.5
24.1
0.982204
Jupiter
5.2
13.1
1.006056
Saturn
9.6
9.7
1.018335
Uranus
19.2
6.8
1.000910...

1The figure below shows an overhead view of a
ring that can rotate about its center like a merry-go-round. Its
outer radius R2 is 0.770 m, its inner radius
R1 is R2/2.00, its mass
M is 8.70 kg, and the mass of the crossbars at its center
is negligible. It initially rotates at an angular speed of 7.80
rad/s with a cat of mass m = M/4.00 on its outer
edge, at radius R2. By how much does the cat...

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