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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?

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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] .

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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 × 10 30 kg size 12{1 "." "98" times "10" rSup { size 8{"30"} } "kg"} {}

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

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

M J M E = 316 size 12{ { {M rSub { size 8{J} } } over {M rSub { size 8{E} } } } ="316"} {}

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Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8 . 0 × 10 11 size 12{8 "." 0 times "10" rSup { size 8{"11"} } } {} solar masses. A star orbiting on the galaxy’s periphery is about 6 . 0 × 10 4 size 12{6 "." 0 times "10" rSup { size 8{4} } } {} light years from its center. (a) What should the orbital period of that star be? (b) If its period is 6 . 0 × 10 7 size 12{6 "." 0 times "10" rSup { size 8{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.

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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 90º size 12{"90" rSup { size 8{ circ } } } {} 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 . 4 × 10 3 m/s size 12{2 "." "11" times "10" rSup { size 8{4} } `"m/s"} {}

b) 1 . 05 × 10 3 m/s size 12{2 "." "98" times "10" rSup { size 8{4} } `"m/s"} {}

c) 2 . 86 × 10 7 s size 12{1 "." "01" times "10" rSup { size 8{ - 7} } s} {}

d) 1 . 84 × 10 7 N size 12{1 "." "48" times "10" rSup { size 8{3} } s} {}

e) 2 . 76 × 10 4 J size 12{2 "." "22" times "10" rSup { size 8{5} } J} {}

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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 . 08 × 10 3 km size 12{5 "." "08" times "10" rSup { size 8{3} } `"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.

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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.

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Questions & Answers

basically potentiometer is series circuit or parallel circuit?
muhammad Reply
What is half-life
Godwin Reply
the life in which half of the radioactive element decay
Arif
what is fluid
Anthony Reply
anything that flows is Liquid.
prakash
a substance that has no specific shape
Saleemulhaq
How submarines floats one water the same time sink in water
Courage Reply
A submarine has the ability to float and sink. The ability to control buoyancy comes from the submarine'strim or ballast tanks which can be filled with either water or air, depending on whether the submarine needs to floator sink. When the submarine floats it means its trim tanks are filled with air
Arif
define electromagnetic radiation
Anthony
what is work
Ojo Reply
Force times distance
Karanja
product of force and distance...
Arif
Is physics a natural science?
Adebisi Reply
what is the difference between a jet engine and a rocket engine.
Samuel Reply
explain the relationship between momentum and force
Joseph Reply
A moment is equivalent multiplied by the length passing through the point of reaction and that is perpendicular to the force
Karanja
How to find Squirrel frontal area from it's surface area?
Pooja Reply
how do we arrange the electronic configuration of elements
Muhammed Reply
hi guys i am an elementary student
benedict Reply
hi
Dancan
hello
adolphus
are you an elementary student too?
benedict
no bro
adolphus
yes
Che
hi
Miranwa
yes
Miranwa
welcome
Miranwa
what is the four equation of motion
Miranwa
what is strain?
SAMUEL
Change in dimension per unit dimension is called strain. Ex - Change in length per unit length l/L.
ABHIJIT
strain is the ratio of extension to length..=e/l...it has no unit because both are in meters and they cancel each other
adeleke
How is it possible for one to drink a cold drink from a straw?
Karanja Reply
most possible as it is for you to drink your wine from your straw
Selina
state the law of conservation of energy
Sushma Reply
energy can neither be destroy or created,but can be change from one form to another
dare
yeah
Toheeb
it can neither be created nor destroyed
Toheeb
its so sample question dude
Muhsin
what is the difference between a principle and a law?
Mary Reply
where are from you wendy .?
ghulam
philippines
Mary
why?
Mary
you are beautiful
ghulam
are you physics student
ghulam
laws are ment to be broken
Ge
hehe ghulam where r u from?
Muhsin
yes
dare
principle are meant to be followed
dare
south Africa
dare
here Nigeria
Toheeb
principle is a rule or law of nature, or the basic idea on how the laws of nature are applied.
Ayoka
Rules are meant to be broken while principals to be followed
Karanja
principle is a rule or law of nature, or the basic idea on how the laws of nature are applied.
tathir
what is momentum?
prakash Reply
is the mass times velocity of an object
True
it is the product of mass and velocity of an object.
The momentum possessed by a body is generally defined as the product of its mass and velocity m×v
Usman
momentum is the product of the mass of a body of its velocity
Ugbesia

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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