6.6 Satellites and kepler’s laws: an argument for simplicity  (Page 4/5)

 Page 4 / 5

A non-satellite body fulfilling only the first two of the above criteria is classified as “dwarf planet.”

In 2006, Pluto was demoted to a ‘dwarf planet’ after scientists revised their definition of what constitutes a “true” planet.

Orbital data and kepler’s third law
Parent Satellite Average orbital radius r (km) Period T(y) r 3 / T 2 (km 3 / y 2 )
Earth Moon $3.84×{\text{10}}^{5}$ 0.07481 $1\text{.}\text{01}×{\text{10}}^{\text{19}}$
Sun Mercury $5\text{.}\text{79}×{\text{10}}^{7}$ 0.2409 $3\text{.}\text{34}×{\text{10}}^{\text{24}}$
Venus $1\text{.}\text{082}×{\text{10}}^{8}$ 0.6150 $3\text{.}\text{35}×{\text{10}}^{\text{24}}$
Earth $1\text{.}\text{496}×{\text{10}}^{8}$ 1.000 $3\text{.}\text{35}×{\text{10}}^{\text{24}}$
Mars $2\text{.}\text{279}×{\text{10}}^{8}$ 1.881 $3\text{.}\text{35}×{\text{10}}^{\text{24}}$
Jupiter $7\text{.}\text{783}×{\text{10}}^{8}$ 11.86 $3\text{.}\text{35}×{\text{10}}^{\text{24}}$
Saturn $1\text{.}\text{427}×{\text{10}}^{9}$ 29.46 $3\text{.}\text{35}×{\text{10}}^{\text{24}}$
Neptune $4\text{.}\text{497}×{\text{10}}^{9}$ 164.8 $3\text{.}\text{35}×{\text{10}}^{\text{24}}$
Pluto $5\text{.}\text{90}×{\text{10}}^{9}$ 248.3 $3\text{.}\text{33}×{\text{10}}^{\text{24}}$
Jupiter Io $4\text{.}\text{22}×{\text{10}}^{5}$ 0.00485 (1.77 d) $3\text{.}\text{19}×{\text{10}}^{\text{21}}$
Europa $6\text{.}\text{71}×{\text{10}}^{5}$ 0.00972 (3.55 d) $3\text{.}\text{20}×{\text{10}}^{\text{21}}$
Ganymede $1\text{.}\text{07}×{\text{10}}^{6}$ 0.0196 (7.16 d) $3\text{.}\text{19}×{\text{10}}^{\text{21}}$
Callisto $1\text{.}\text{88}×{\text{10}}^{6}$ 0.0457 (16.19 d) $3\text{.}\text{20}×{\text{10}}^{\text{21}}$

The universal law of gravitation is a good example of a physical principle that is very broadly applicable. That single equation for the gravitational force describes all situations in which gravity acts. It gives a cause for a vast number of effects, such as the orbits of the planets and moons in the solar system. It epitomizes the underlying unity and simplicity of physics.

Before the discoveries of Kepler, Copernicus, Galileo, Newton, and others, the solar system was thought to revolve around Earth as shown in [link] (a). This is called the Ptolemaic view, for the Greek philosopher who lived in the second century AD. This model is characterized by a list of facts for the motions of planets with no cause and effect explanation. There tended to be a different rule for each heavenly body and a general lack of simplicity.

[link] (b) represents the modern or Copernican model. In this model, a small set of rules and a single underlying force explain not only all motions in the solar system, but all other situations involving gravity. The breadth and simplicity of the laws of physics are compelling. As our knowledge of nature has grown, the basic simplicity of its laws has become ever more evident.

Section summary

• Kepler’s laws are stated for a small mass $m$ orbiting a larger mass $M$ in near-isolation. Kepler’s laws of planetary motion are then as follows:

Kepler’s first law

The orbit of each planet about the Sun is an ellipse with the Sun at one focus.

Kepler’s second law

Each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal areas in equal times.

Kepler’s third law

The ratio of the squares of the periods of any two planets about the Sun is equal to the ratio of the cubes of their average distances from the Sun:

where $T$ is the period (time for one orbit) and $r$ is the average radius of the orbit.

• The period and radius of a satellite’s orbit about a larger body $M$ are related by
${T}^{2}=\frac{{4\pi }^{2}}{\text{GM}}{r}^{3}$

or

$\frac{{r}^{3}}{{T}^{2}}=\frac{G}{{4\pi }^{2}}M\text{.}$

write an expression for a plane progressive wave moving from left to right along x axis and having amplitude 0.02m, frequency of 650Hz and speed if 680ms-¹
how does a model differ from a theory
what is vector quantity
Vector quality have both direction and magnitude, such as Force, displacement, acceleration and etc.
Besmellah
Is the force attractive or repulsive between the hot and neutral lines hung from power poles? Why?
what's electromagnetic induction
electromagnetic induction is a process in which conductor is put in a particular position and magnetic field keeps varying.
Lukman
wow great
Salaudeen
what is mutual induction?
je
mutual induction can be define as the current flowing in one coil that induces a voltage in an adjacent coil.
Johnson
how to undergo polarization
show that a particle moving under the influence of an attractive force mu/y³ towards the axis x. show that if it be projected from the point (0,k) with the component velocities U and V parallel to the axis of x and y, it will not strike the axis of x unless u>v²k² and distance uk²/√u-vk as origin
show that a particle moving under the influence of an attractive force mu/y^3 towards the axis x. show that if it be projected from the point (0,k) with the component velocities U and V parallel to the axis of x and y, it will not strike the axis of x unless u>v^2k^2 and distance uk^2/√u-k as origin
No idea.... Are you even sure this question exist?
Mavis
I can't even understand the question
yes it was an assignment question "^"represent raise to power pls
Gabriel
Gabriel
An engineer builds two simple pendula. Both are suspended from small wires secured to the ceiling of a room. Each pendulum hovers 2 cm above the floor. Pendulum 1 has a bob with a mass of 10kg . Pendulum 2 has a bob with a mass of 100 kg . Describe how the motion of the pendula will differ if the bobs are both displaced by 12º .
no ideas
Augstine
if u at an angle of 12 degrees their period will be same so as their velocity, that means they both move simultaneously since both both hovers at same length meaning they have the same length
Modern cars are made of materials that make them collapsible upon collision. Explain using physics concept (Force and impulse), how these car designs help with the safety of passengers.
calculate the force due to surface tension required to support a column liquid in a capillary tube 5mm. If the capillary tube is dipped into a beaker of water
find the time required for a train Half a Kilometre long to cross a bridge almost kilometre long racing at 100km/h
method of polarization
Ajayi
What is atomic number?
The number of protons in the nucleus of an atom
Deborah
type of thermodynamics
oxygen gas contained in a ccylinder of volume has a temp of 300k and pressure 2.5×10Nm
why the satellite does not drop to the earth explain
what is a matter
Yinka
what is matter
Yinka
what is matter
Yinka
what is a matter
Yinka
I want the nuclear physics conversation
Mohamed
because space is a vacuum and anything outside the earth 🌎 can not come back without an act of force applied to it to leave the vacuum and fall down to the earth with a maximum force length of 30kcm per second
Clara