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

 Page 5 / 5

## Conceptual questions

In what frame(s) of reference are Kepler’s laws valid? Are Kepler’s laws purely descriptive, or do they contain causal information?

## Problem exercises

A geosynchronous Earth satellite is one that has an orbital period of precisely 1 day. Such orbits are useful for communication and weather observation because the satellite remains above the same point on Earth (provided it orbits in the equatorial plane in the same direction as Earth’s rotation). Calculate the radius of such an orbit based on the data for the moon in [link] .

Calculate the mass of the Sun based on data for Earth’s orbit and compare the value obtained with the Sun’s actual mass.

$1.98×{\text{10}}^{\text{30}}\phantom{\rule{0.25em}{0ex}}\text{kg}$

Find the mass of Jupiter based on data for the orbit of one of its moons, and compare your result with its actual mass.

Find the ratio of the mass of Jupiter to that of Earth based on data in [link] .

$\frac{{M}_{J}}{{M}_{E}}=\text{316}$

Astronomical observations of our Milky Way galaxy indicate that it has a mass of about $8\text{.}0×{\text{10}}^{\text{11}}$ solar masses. A star orbiting on the galaxy’s periphery is about $6\text{.}0×{\text{10}}^{4}$ light years from its center. (a) What should the orbital period of that star be? (b) If its period is $6\text{.}0×{\text{10}}^{7}$ instead, what is the mass of the galaxy? Such calculations are used to imply the existence of “dark matter” in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies.

Integrated Concepts

Space debris left from old satellites and their launchers is becoming a hazard to other satellites. (a) Calculate the speed of a satellite in an orbit 900 km above Earth’s surface. (b) Suppose a loose rivet is in an orbit of the same radius that intersects the satellite’s orbit at an angle of $\text{90º}$ relative to Earth. What is the velocity of the rivet relative to the satellite just before striking it? (c) Given the rivet is 3.00 mm in size, how long will its collision with the satellite last? (d) If its mass is 0.500 g, what is the average force it exerts on the satellite? (e) How much energy in joules is generated by the collision? (The satellite’s velocity does not change appreciably, because its mass is much greater than the rivet’s.)

a) $7\text{.}\text{4}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{m/s}$

b) $1\text{.}\text{05}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{m/s}$

c) $2\text{.}\text{86}×{\text{10}}^{-7}\phantom{\rule{0.25em}{0ex}}\text{s}$

d) $1\text{.}\text{84}×{\text{10}}^{7}\phantom{\rule{0.25em}{0ex}}\text{N}$

e) $2\text{.}\text{76}×{\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}\text{J}$

Unreasonable Results

(a) Based on Kepler’s laws and information on the orbital characteristics of the Moon, calculate the orbital radius for an Earth satellite having a period of 1.00 h. (b) What is unreasonable about this result? (c) What is unreasonable or inconsistent about the premise of a 1.00 h orbit?

a) $5\text{.}\text{08}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{km}$

b) This radius is unreasonable because it is less than the radius of earth.

c) The premise of a one-hour orbit is inconsistent with the known radius of the earth.

Construct Your Own Problem

On February 14, 2000, the NEAR spacecraft was successfully inserted into orbit around Eros, becoming the first artificial satellite of an asteroid. Construct a problem in which you determine the orbital speed for a satellite near Eros. You will need to find the mass of the asteroid and consider such things as a safe distance for the orbit. Although Eros is not spherical, calculate the acceleration due to gravity on its surface at a point an average distance from its center of mass. Your instructor may also wish to have you calculate the escape velocity from this point on Eros.

#### Questions & Answers

Calculate the work done by an 85.0-kg man who pushes a crate 4.00 m up along a ramp that makes an angle of 20.0º20.0º with the horizontal. (See [link] .) He exerts a force of 500 N on the crate parallel to the ramp and moves at a constant speed. Be certain to include the work he does on the crate an
What is thermal heat all about
why uniform circular motion is called a periodic motion?.
when a train start from A & it returns at same station A . what is its acceleration?
what is distance of A to B of the stations and what is the time taken to reach B from A
BELLO
the information provided is not enough
aliyu
Hmmmm maybe the question is logical
yusuf
where are the parameters for calculation
HENRY
there is enough information to calculate an AVERAGE acceleration
Kwok
mistake, there is enough information to calculate an average velocity
Kwok
~\
Abel
what is the unit of momentum
Abel
wha are the types of radioactivity ?
what are the types of radioactivity
Worku
what is static friction
It is the opposite of kinetic friction
Mark
static fiction is friction between two surfaces in contact an none of sliding over on another, while Kinetic friction is friction between sliding surfaces in contact.
MINDERIUM
I don't get it,if it's static then there will be no friction.
author
It means that static friction is that friction that most be overcome before a body can move
kingsley
static friction is a force that keeps an object from moving, and it's the opposite of kinetic friction.
author
It is a force a body must overcome in order for the body to move.
Eboh
If a particle accelerator explodes what happens
Eboh
why we see the edge effect in case of the field lines of capacitor?
Arnab
what is wave
what is force
Muhammed
force is something which is responsible for the object to change its position
MINDERIUM
more technically it is the product of mass of an object and Acceleration produced in it
MINDERIUM
wave is disturbance in any medium
iqra
energy is distributed in any medium through particles of medium.
iqra
If a particle accelerator explodes what happens
we have to first figure out .... wats a particle accelerator first
Teh
What is surface tension
The resistive force of surface.
iqra
Who can tutor me on simple harmonic motion
on both a string and peldulum?
Anya
spring*
Anya
Yea
yusuf
Do you have a chit-chat contact
yusuf
I dont have social media but i do have an email?
Anya
Which is
yusuf
Where are you chatting from
yusuf
I don't understand the basics of this group
Jimmy
teach him SHM init
Anya
Simple harmonic motion
yusuf
how.an.equipotential.line is two dimension and equipotential surface is three dimension ?
definition of mass of conversion
Force equals mass time acceleration. Weight is a force and it can replace force in the equation. The acceleration would be gravity, which is an acceleration. To change from weight to mass divide by gravity (9.8 m/s^2).
Marisa
how many subject is in physics
the write question should be " How many Topics are in O- Level Physics, or other branches of physics.
effiom
how many topic are in physics
Praise
Praise what level are you
yusuf
If u are doing a levels in your first year you do AS topics therefore you do 5 big topic i.e particles radiation, waves and optics, mechanics,materials, electricity. After that you do A level topics like Specific Harmonic motion circular motion astrophysics depends really
Anya
Yeah basics of physics prin8
yusuf
Heat nd Co for a level
yusuf
yh I need someone to explain something im tryna solve . I'll send the question if u down for it
a ripple tank experiment a vibrating plane is used to generate wrinkles in the water .if the distance between two successive point is 3.5cm and the wave travel a distance of 31.5cm find the frequency of the vibration
Tamdy
hallow
Boniface
Boniface
the range of objects and phenomena studied in physics is
I don't know please give the answer
Boniface