# 10.5 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

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

what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!