The discovery of Electron and the Plum Budding Model

Before 1897, the atom model was believed to be a solid sphere. Thomson then disagreed with this idea.

He conducted an experiment by producing a visible beam called a cathode ray in a tube. He also placed two plates with opposite charges around the beam and two magnets on either side of the tube. The result showed that:

• The particles are attracted by positive (+) charges and repelled by negative (−) charges, so they must be negatively charged
• They exist as a part of the atom and are less massive than atoms regardless of the source material
• These subatomic particles can be found within atoms of all elements

Electrons were found like this. He later proposed that atoms can be described as negative particles floating within a soup of diffuse positive charge. The model was known as the Plum Pudding model.

How is the evidence of the Universe developed?

In the early years, the universe is small and extremely hot. All the matter existed as a dense plasma. Plasma—one of four fundamental states after solid, liquid, and gas—absorbed light, making the universe opaque (preventing light from traveling through, therefore not transparent). As the universe expands, so does the matter and energy inside it. What started as light released at that moment has now been stretched into the microwave region. Microwave radiation, WMAP can peer backward in time to when that radiation was emitted.

From 1989 to 1993, COBE tested many theories that predicted by the existence of a Big Bang and collected evidence to develop future questions. The data found agreed with the scientists’ predictions, it left a lot of questions unanswered.

WMAP was launched on June 30, 2001, placed in six-month orbit around the L2 Lagrange point, which is 1.5 million km from Earth. WMAP created an extremely precise full-sky map of the cosmic microwave background, improving upon the maps by COBE.

WMAP answered that the Universe started flat and aged 13.8b years ago. It also showed that dark energy is an unknown force that counteracts gravity, pushing galaxies away from each other rather than causing attract one another as we would expect if gravity were the only force at work.

After 9 year of accumulation, it also helped to prove that the Universe’s expansion is accelerating.

Bullet Cluster (4b years ago)

The image depicts a duo of clusters of galaxies as observed through the Chandra X-ray observatory. The red shading represents the ordinary gas that has become hot, while the blue shading represents the presence of dark matter, which is figured out by looking at the gravitational lensing effect.

So why is it? Because the cluster of galaxies is basically an ocean of dark matter, which is supposed to keep the galaxies and gas inside. However, this gas is sort of outside of the ocean of dark matter. After some studies, it turned out that this was the aftermath of a collision of two clusters at an incredible speed of 45000 km/s.

During the collision of two clusters, the gas within them indeed interacts, leading to heating and friction, which causes them to decelerate and remain behind due to gravitational pull. However, dark matter continues to move as though unaffected by the collision.

Why do distant Galaxies look red? Is it because they are expanding?

An example with sound

A simple explanation comes from the pitch of sound. When an ambulance is passing in front of you the pitch is going up. Imagine an ambulance is approaching close to you, the pitch of the siren will be going up. When it passes through and far away (receding) from you, the pitch will be going down. From these observations, we can draw some comments:

• Approaching object gives away high pitch sound
• Receding object gives away low pitch sound
• Receding star gives away red color

Similarly, if a star is moving far away from the Earth, the light that a telescope captures from the star turns red.

This is called Doppler effect, and now comes the calculation:

f’ = V / (V + v) x f (when the object letting the sound out is moving)

f’ = (V - v) / V x f (when the object is moving, relative to the air)

Where:

V is the speed of sound and v is the speed of the object perceiving the sound.

Consider the example: a police car is moving west at 20m/s toward a driver who is moving east at 25m/s. The police car emits a frequency of 900 Hz. What frequency is detected by the driver? Given the speed of sound in air at 20C is 343m/s.

In case of light

f’ = square root of((V - v) / (V + v)) x f where V is the speed of light and v is the relative speed between the object producing light and receiving light.

Yes, the Universe is expanding

The Universe is not static, it rather exists in 3 possible states: warp, twist, and expand. Today, more and more evidence, especially redshift, verifies the expansion theory throughout the observable universe. As a result, the Universe as a whole is getting bigger and, at the same time, getting colder. When returning to the past (Big Bang), it was smaller and hotter.

E = hv = hc / lambda (h is Planck constant)

Revolution of the Earth

Ptolemy and the ancient observation

The ancient observation explains that we are at the center of the universe and any other star revolves around us. The observation is true for the Moon and Sun but wired for the other planets like Mercury, Venus, Saturn, and so on.

They saw that these planets also moves back and forth around us. In order to explain this, they added the concept of epicycle motion. Over time, they realized it is not true and trying to add more epicycle and making things more complicated. They started to think that the Universe cannot this be complex understanding and this idea is possibly right.

Copernicus and the modern observation

Copernicus, he believed that there is another simpler explanation and completely changed the idea of observation. He stated that the Sun is actually at the center and the Earth off-center along with other planets moving around the Sun in complete circles.

Let’s take Saturn as an example, because Earth and Saturn move at different speed where the Earth is faster, we would see the Saturn is a little bit falling behind. And when the Earth comes back from the other side, we see the Saturn is moving ahead.

Kepler and the Elliptical orbits

Everything still does not agree with the observations as the data collected are so precise. Kepler came up with another single concept that the orbits are elliptical and this very well explains the observations that meet all the criteria for a good physical theory.

1. Agree with observations and experiments
2. Has a unified description
3. And simple

Newton’s second law of motion and Universal law of gravitation in combination well explain the elliptical motion of a planet.

• F = ma means net force is equal to mass times acceleration.
• F = G(Mm)/square(R) means the gravitational force (F) of two masses M (the Earth) and m (satellite/planet) is inversely proportional to the square of distance (R) between them.

Newton’s second law of motion describes how difficult it is to influence the course of motion. An example of this is when a car and a bicycle in stationary motion are provided the same push, it is more likely for the bicycle to move. The Universal Law of Gravitation shows how strongly it is pulled by the force of gravity. If m (a satellite/planet) gets closer to M (the Earth), the force (F) increases, and so does the acceleration (a).

Kepler’s three laws:

1. The orbit of every planet is an ellipse with the Sun at one of the two foci.
2. A line running from the sun to the planet sweeps out equal areas of the ellipse in equal times.
3. The square of the orbital period of a planet is directly proportional to the cube of the radius of its orbit.

As the Sun is extremely massive and accounts for 99,86% total mass of the Solar system, I also wonder if Kepler’s laws hold true in similar cases. If the ratio of mass between the Moon and Earth is established, 1.2%, we can easily come up with the idea that Earth-Moon system satisfies all the conditions to obey Kepler’s laws. However, thinking a small body in term of mass on a stable orbit hinders us from realising that it is attracted by more than one body. In fact, it is, and one of them has the strongest and significant gravitational force over others that leads to the study of 2-body problem. This is a great reference as it also mentions the 2nd condition to consider due to n-body problem. The condition is what many resources do not explicitly point out perhaps because when describing planetary systems in Solar system, they assume that these systems are isolated. In this context, I prefer the phrase “nearly isolated” as one body is more or less still under gravitational influence of many other bodies.

1. The orbiting mass is small compared to the mass it orbits.
2. The system is isolated from other large masses.

Lagrange point is a special point where a small mass is under gravitational force of 2 massive bodies. For every 2-body system, there are 5 points such that the gravitational forces balance each other and reach equilibrium. These have been the ideal positions to place artificial statellites for a long time.

A bit of thermodynamics

Regarding the concept of isolated system, it reminds me of lessons about thermodynamics that deal with work, heat, energy, and open, closed, or isolated system using algebra-based physics in high school. Many of these can be easily experienced when preparing dishes as kitchen is the best chemistry lab after school. It is easily observed that closed and isolated systems have the distribution being shifted to higher velocity (higher kinetic energy) and flattened when temperature is increased. Because open systems exchange matter and energy with their surroundings, they are considered non-equilibrium. The ocean is a typical example of an open system, where energy from solar radiation and matter are exchanged with the atmosphere above.

Temperature, pressure, amount, and volume are closely related, and their interactions give rise to four fundamental laws of an ideal gas system. Changes in one of these variables directly influence the others. In a closed or isolated system with a fixed volume, an increase in temperature results in kinetic energy and so forth pressure. If a system of liquid and gas produces additional gas particles as product but does not results in significantly reduction of reactants that leads to higher density of gas, pressure also increases. These changes are not observable at the level of individual particles but happen when considering a large number of them, an example of emergent properties. These properties are also very important inputs when filing a flight plan, especially takeoff and landing performance.

If algebra represents the relationship between variables, calculus captures, for example, the rate of change in motion of planet as the world also exhibits non-linearity.