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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

What is conductivity
Saud Reply
It is the ease with which electrical charges or heat can be transmitted through a material or a solution.
Cffrrcvccgg
how to find magnitude and direction
Arjune Reply
how to caclculate for speed
Arjune
derivation of ohms law
Kazeem Reply
derivation of resistance
Kazeem
R=v/I where R=resistor, v=voltage, I=current
Kazeem
magnitude
Arjune
A puck is moving on an air hockey table. Relative to an x, y coordinate system at time t 0 s, the x components of the puck’s ini￾tial velocity and acceleration are v0x 1.0 m/s and ax 2.0 m/s2 . The y components of the puck’s initial velocity and acceleration are v0y 2.0 m/s and ay 2.0
Arjune
Electric current is the flow of electrons
Kelly Reply
is there really flow of electrons exist?
babar
Yes It exists
Cffrrcvccgg
explain plz how electrons flow
babar
if electron flows from where first come and end the first one
babar
an electron will flow accross a conductor because or when it posseses kinectic energy
Cffrrcvccgg
electron can not flow jist trasmit electrical energy
ghulam
free electrons of conductor
ankita
electric means the flow heat current.
Serah Reply
electric means the flow of heat current in a circuit.
Serah
What is electric
Manasseh Reply
electric means?
ghulam
electric means the flow of heat current in a circuit.
Serah
a boy cycles continuously through a distance of 1.0km in 5minutes. calculate his average speed in ms-1(meter per second). how do I solve this
Jenny Reply
speed = distance/time be sure to convert the km to m and minutes to seconds check my utube video "mathwithmrv speed"
PhysicswithMrV
d=1.0km÷1000=0.001 t=5×60=300s s=d\t s=0.001/300=0.0000033m\s
Serah
A puck is moving on an air hockey table. Relative to an x, y coordinate system at time t 0 s, the x components of the puck’s ini￾tial velocity and acceleration are v0x 1.0 m/s and ax 2.0 m/s2 . The y components of the puck’s initial velocity and acceleration are v0y 2.0 m/s and ay 2.0
Arjune
why we cannot use DC instead of AC in a transformer
kusshaf Reply
becuse the d .c cannot travel for long distance trnsmission
ghulam
what is physics
Chiwetalu Reply
branch of science which deals with matter energy and their relationship between them
ghulam
Life science
the
what is heat and temperature
Kazeem Reply
how does sound affect temperature
Clement Reply
sound is directly proportional to the temperature.
juny
how to solve wave question
Wisdom Reply
I would like to know how I am not at all smart when it comes to math. please explain so I can understand. sincerly
Emma
Just know d relationship btw 1)wave length 2)frequency and velocity
Talhatu
First of all, you are smart and you will get it👍🏽... v = f × wavelength see my youtube channel: "mathwithmrv" if you want to know how to rearrange equations using the balance method
PhysicswithMrV
nice self promotion though xD
Beatrax
thanks dear
Chuks
hi pls help me with this question A ball is projected vertically upwards from the top of a tower 60m high with a velocity of 30ms1.what is the maximum height above the ground level?how long does it take to reach the ground level?
mahmoud
please guys help, what is the difference between concave lens and convex lens
Vincent Reply
convex lens brings rays of light to a focus while concave diverges rays of light
Christian
for mmHg to kPa yes
Matthew
it depends on the size
Matthew Reply
please what is concave lens
Vincent
a lens which diverge the ray of light
rinzuala
concave diverges light
Matthew
thank you guys
Vincent
A diverging lens
Yusuf
What is isotope
Yusuf
each of two or more forms of the same element that contain equal numbers of protons but different numbers of neutrons in their nuclei, and hence differ in relative atomic mass but not in chemical properties; in particular, a radioactive form of an element. "some elements have only one stable isotope
Karthi
what is wire wound resistors?
Naveedkhan Reply

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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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