# 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

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

is there more then 4 dimensions
hii
princy
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Miguel
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Brown
Brown. what kind of help
Jeff
when it comes to physics stick with the basics don't overthink things
Jeff
yes
ayesha
sticking to the basics will take you farther than overwhelming yourself with more than you need to physics is simple keep it simple
Jeff
thk u Ayesha
Jeff
for real....? so I've got to know the fundamentals and use the formula to solve any problem
Brown
read Stephan hawkings a brief history of time
ayesha
ayesha
physics isn't hard it's just understanding and applying the formulas if u need help ask any question
ayesha
okay...because I've got an exam next year February a Computer based exam
Brown
ayesha
ayesha
how can we find absolute uncertainty
it what?
Luke
in physics
ayesha
the basic formula is uncertainty in momentum multiplied buy uncertainty In position is greater than or equal to 4×pi/2. same formula for energy and time
Luke
I have this one question can you please look it up it's 9702/22/O/N/17 Question 1 B 3
ayesha
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uma
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Suthar
yes
farooq
precision or absolute uncertainty is always equal to least count of that instrument
Iram
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what is the dimension of strain
Is there a formula for time of free fall given that the body has initial velocity? In other words, formula for time that takes a downward-shot projectile to hit the ground. Thanks!
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Agboro
hiii
Chandan
Hi
Sahim
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Jeff
hey
Priscilla
sup guys
Bile
Hy
Kulsum
What is unit of watt?
Kulsum
watt is the unit of power
Rahul
p=f.v
Rahul
watt can also be expressed as Nm/s
Rahul
what s i unit of mass
Maxamed
SI unit of mass is Kg(kilogram).
Robel
what is formula of distance
Maxamed
Formula for for the falling body with initial velocity is:v^2=v(initial)^2+2*g*h
Mateo
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Maxamed
we can't do this calculation without knowing the height of the initial position of the particle
Chathu
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Imoreh
2 forces whose resultant is 100N, are at right angle to each other .if one of them makes an angle of 30 degree with the resultant determine it's magnitude
50 N... (50 *1.732)N
Sahim
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Sahim
50 N...(50 *1.732)N
Ibrahim
show the working
usiomon
what is the value of f1 and f2
Syed
what is the value of force 1 and force 2.
Syed
.
Is earth is an inertial frame?
The abacus (plural abaci or abacuses), also called a counting frame, is a calculating tool that was in use in Europe, China and Russia, centuries before the adoption of the written Hindu–Arabic numeral system
Sahim
thanks
Irungu
Most welcome
Sahim
Hey.. I've a question.
Is earth inertia frame?
Sahim
only the center
Shii
What is an abucus?
Irungu
what would be the correct interrogation "what is time?" or "how much has your watch ticked?"
prakash
a load of 20N on a wire of cross sectional area 8×10^-7m produces an extension of 10.4m. calculate the young modules of the material of the wire is of length 5m
Young's modulus = stress/strain strain = extension/length (x/l) stress = force/area (F/A) stress/strain is F l/A x
El
so solve it
Ebenezer
Ebenezer
two bodies x and y start from rest and move with uniform acceleration of a and 4a respectively. if the bodies cover the same distance in terms of tx and ty what is the ratio of tx to ty
what is cesium atoms?
The atoms which form the element Cesium are known as Cesium atoms.
Naman
A material that combines with and removes trace gases from vacuum tubes.
Shankar
what is difference between entropy and heat capacity
Varun
Heat capacity can be defined as the amount of thermal energy required to warm the sample by 1°C. entropy is the disorder of the system. heat capacity is high when the disorder is high.
Chathu
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Vinodhini
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Vinodhini
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What is realm
The quantum realm, also called the quantum scale, is a term of art inphysics referring to scales where quantum mechanical effects become important when studied as an isolated system. Typically, this means distances of 100 nanometers (10−9meters) or less or at very low temperature.
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