to what radius would the sun have to be contracted for its escape speed to equal the speed of light?

Mastering Physics Solutions Chapter 12 Gravity

Mastering Physics Solutions

Chapter 12 Gravity Q.1CQ
It is often said that astronauts in orbit experience weightlessness because they are beyond the pull of Earth's gravity. Is this statement right? Explicate.
Solution:
No The force of Earth'southward gravity is practically as potent in orbit every bit information technology is on the surface of Earth The astronauts feel weightlessness because they are in constant free autumn.

Chapter 12 Gravity Q.1P
CE System A has masses grand and thousand separated by a distance r; organization B has masses g and 2m separated past a distance 2r; system C has masses 2m and 3m separated by a distance 2r, and system D has masses 4m and 5m separated past a altitude 3r. Rank these systems in club of increasing gravitational force. Indicate ties where appropriate.
Solution:

Affiliate 12 Gravity Q.2CQ
When a person passes you on the street, you practise not experience a gravitational tug. Explain.
Solution:

Chapter 12 Gravity Q.2P
In each hand you hold a 0.16-kg apple. What is the gravitational force exerted by each apple on the other when their separation is (a) 0.25 g and (b) 0.50 k?
Solution:

Chapter 12 Gravity Q.3CQ
2 objects experience a gravitational allure. Give a reason why the gravitational strength between them does not depend on the sum of their masses.
Solution:
The force of gravity between two point masses m1 and m2, separated past a distance r, is attractive and of magnitude

where G is the universal gravitational constant.
Gravity exerts an action-reaction pair of forces on m1 and m2. That is, the force exerted by gravity on m1 is equal in magnitude only opposite in direction to the force exerted on m2. It is dependent on the product of masses. If the gravitational strength depended on the sum of the two masses, it would predict a non-zero strength even when one of the masses is zero. That is, there would exist a gravitational force betwixt a mass and a point in empty space, which is certainly not what we observed.

Chapter 12 Gravity Q.3P
A half dozen.1-kg bowling ball and a 7.2-kg bowling brawl rest on a rack 0.75 g apart. (a) What is the forcefulness of gravity exerted on each of the balls by the other ball? (b) At what separation is the force of gravity between the assurance equal to 2.0 × x?9N?
Solution:

Affiliate 12 Gravity Q.4CQ
Imagine bringing the tips of your alphabetize fingers together. Each finger contains a certain finite mass, and the altitude betwixt them goes to zero every bit they come up into contact. From the strength law F = Gm1m2/r2 one might conclude that the attractive force between the fingers is infinite, and, therefore, that your fingers must remain forever stuck together. What is wrong with this statement?
Solution:
As the tips of the fingers approach one another, we can think of them as existence two small spheres that impact each other. Even though the 2 spheres touch each other, the distance between the centers is non cypher. This is always a finite number. Therefore, the force betwixt the spheres is always finite, fifty-fifty they touch each other. As such, the two fingers simply experience the finite force of 2 betoken masses separated by a finite distance.

Chapter 12 Gravity Q.4P
A communications satellite with a mass of 480 kg is in a round orbit about the Earth. The radius of the orbit is 35,000 km as measured from the center of the Earth. Calculate (a) the weight of the satellite on the surface of the World and (b) the gravitational force exerted on the satellite by the Earth when it is in orbit.
Solution:

Affiliate 12 Gravity Q.5CQ
Does the radius vector of Mars sweep out the same amount of surface area per time as that of the Globe? Why or why not?
Solution:
No. The amount of surface area swept out per time varies from planet to planet because the linear speeds of planets are unlike.

Chapter 12 Gravity Q.5P
The Attraction of Ceres Ceres, the largest asteroid known, has a mass of roughly 8.vii × 1020 kg. If Ceres passes within 14,000 km. of the spaceship in which you are traveling, what force does it exert on you? (Utilize an approximate value for your mass, and treat yourself and the asteroid as signal objects.)
Solution:

Chapter 12 Gravity Q.6CQ
When a communications satellite is placed in a geosynchronous orbit above the equator. it remains fixed over a given point on the footing. Is it possible to put a satellite into an orbi t so that information technology remains fixed in a higher place the North Pole? Explicate
Solution:
INot possiblel because a satellite will appear stationary just when information technology revolves in an orbit that is concentric and coplanar with the equatorial plane, has a catamenia of revolution of 24 hours, and
has a sense of revolution from the west to the east of Globe. As the n pole is abroad from the equatorial plane. it will not be possible to put a geostationary satellite over the north pole.

Chapter 12 Gravity Q.6P
In ane manus you hold a 0.eleven-kg apple, in the other hand a 0.24-kg orangish. The apple and orange are separated past 0.85 one thousand. What is the magnitude of the forcefulness of gravity that (a) the orange exerts on the apple and (b) the apple exerts on the orangish?
Solution:

Chapter 12 Gravity Q.7CQ
The Mass of Pluto On June 22, 1978, James Christy made the get-go observation of a moon orbiting Pluto. Until that lime the mass of Pluto was not known, but with the discovery of its moon, Charon, its mass could exist calculated with some accuracy. Explain.
Solution:

Affiliate 12 Gravity Q.7P
IP A spaceship of mass m travels from the Earth to the Moon along a line that passes through the eye of the World and the center of the Moon. (a) At what distance from the middle of the World is the force due to the Earth twice the magnitude of the forcefulness due to the Moon? (b) How does your answer to office (a) depend on the mass of the spaceship? Explain.
Solution:

Chapter 12 Gravity Q.8CQ
Rockets arc launched into space from Cape Canaveral in an easterly direction Is there an advantage to launching to the east versus launching to the west? Explain
Solution:
Earth revolves from w to e (counterclockwise) about its polar centrality. Therefore, all the particles on Earth have a velocity from west to e. This velocity is at a maximum along the
equatorial line, as y = Rw,where R is the radius of Earth and w is the angular velocity of Earth'due south revolution about its polar axis.
ICape Canaveral is situated at the equator and then when a rocket is launched from w to east in this place. the maximum linear velocity is added to the launching velocity of the rocket Because of this. launching becomes easied

Affiliate 12 Gravity Q.8P

Solution:

Chapter 12 Gravity Q.9CQ
One 24-hour interval in the futurity you lot may take a pleasance cruise to the Moon While at that place you might climb a lunar mountain and throw a rock horizontally from its summit If. in principle, you could throw the rock fast enough, it might end up hitting you in the back Explicate.
Solution:
Ion the Moon. where there is no atmosphere, a stone can orbit at any altitudel where it clears the mountains — equally long as it has sufficient speed If we could give a rock enough speed. information technology would orbit the Moon and return to usa from the other side (behind).

Affiliate 12 Gravity Q.9P

Solution:

Chapter 12 Gravity Q.10CQ
Apollo astronauts orbiting the Moon at low altitude noticed occasional changes ¡n their orbit that they attributed to localized concentrations of mass below the lunar surface. Only what result would such 'Thascons" have on their orbit?
Solution:
Every bit the astronauts approach a mass concentration, its increased gravitational allure would increment the speed of the craft Similarly, equally they pass the mass concentration, its ravitationaI allure is in the backward direction, which decreases their speed I

Affiliate 12 Gravity Q.10P

Solution:

Affiliate 12 Gravity Q.11CQ
If you calorie-free a candle on the space shuttle—which would non be a skillful idea—would it burn the same as on the Earth? Explain
Solution:
No. In the weightless environment of the shuttle, there is no convection which is required to bring fresh oxygen to the flame. Without convection, a flame commonly goes out very quickly. In carefully controlled experiments on the shuttle, still, small flames take been maintained for considerable times These "weightless" flames are spherical in shape. as opposed to the tear- shaped flames on Earth

Chapter 12 Gravity Q.11P
IP 3 6.75-kg masses are at the corners of an equilateral triangle and located in space far from any other masses. (a) If the sides of the triangle are one.25 thou long, notice the magnitude of the net strength exerted on each of the three masses. (b) How does your answer to role (a) change if the sides of the triangle are doubled in length?
Solution:

Affiliate 12 Gravity Q.12CQ
The forcefulness exerted by the Dominicus on the Moon is more than twice the strength exerted by the Earth on the Moon. Should the Moon be thought of as orbiting the Globe or the Sun? Explain.
Solution:

Chapter 12 Gravity Q.12

Solution:

Chapter 12 Gravity Q.13CQ

Solution:
The net force interim on the moon is ever directed toward the Dominicus, never abroad from the Sunday. Therefore, the Moon'south orbit must ever curve toward the Sunday. It curves sharply toward the Sun when Earth is betwixt the Moon and the Sun, and curves only slightly toward the Sun when the Moon is between the Sun and Earth.

Chapter 12 Gravity Q.13P
Suppose that three astronomical objects (i, 2, and three) are observed to lie on a line, and that the distance from object 1 to object 3 is D. Given that object i. has four times the mass of object 3 and 7 times the mass of object 2, find the distance between objects 1 and ii for which the net forcefulness on object two is zero.
Solution:

Chapter 12 Gravity Q.14P
Discover the acceleration due to gravity on the surface of (a) Mercury and (b) Venus.
Solution:

Chapter 12 Gravity Q.15P
At what altitude above the Earth'due south surface is the acceleration due to gravity equal to grand/two?
Solution:

Chapter 12 Gravity Q.16P
Two vi-7-kg bowling assurance, each with a radius of 0.xi m, are in contact with one another. What is the gravitational attraction between the bowling balls?
Solution:

Chapter 12 Gravity Q.17P
What is the acceleration due to Earth'southward gravity at a distance from the centre of the Globe equal to the orbital radius of the Moon?
Solution:

Chapter 12 Gravity Q.18P
Gravity on Titan Titan is the larges t moon o f Saturn and the merely moon in the solar system known to have a substantial temper. Find the acceleration due to gravity on Titan's surface, given that its mass is 1.35 × 1023 kg and its radius is 2570 km.
Solution:

Affiliate 12 Gravity Q.19P
IP At a certain distance from the centre of the World, a 4.half dozen-kg object has a weight of two.2 N. (a) Observe this distance, (b) If the object is released at this location and allowed to falï toward the Earth, what is its initial acceleration? (c) If the object is at present moved twice as far from the Earth, by what factor does its weight change? Explain, (d) By what factor does its initial acceleration change? Explain.
Solution:

Chapter 12 Gravity Q.20P
Tine acceleration due to gravity on the Moon's surface is known to be about one-sixth the acceleration due to gravity on the Earth. Given that the radius of the Moon is roughly one-quarter that of the Earth, find the mass of the Moon in terms of the mass of the Earth.
Solution:

Chapter 12 Gravity Q.21P
IP An Extraterrestrial Volcano Several volcanoes have been observed erupting on the surface of Jupiter's closest Galilean moon, lo. Suppose that material ejected from one of these volcanoes reaches a superlative of v.00 km a fter existence projected straight upward with an initial speed of 134 g/southward. Given that the radius of lo is 1820 km, (a) outlinca strategy thatallows you to calculate the mass of To. (b) Use your strategy to calculate Io's mass.
Solution:

Chapter 12 Gravity Q.22P
IP Verne's Trip to the Moon In his novel From the Earth to the Moon, Jules Verne imagined that astronauts inside a spaceship would walk on the floor of the cabin when the force exerted on the ship past the Globe was greater than the force exerted past the Moon. When the forcefulness exerted by the Moon was greater, he thought the astronauts would walk on the ceiling of the cabin, (a) At what distance from the center of the Earth would the forces exerted on the spaceship by the Earth and the Moon be equal? (b) Explain why Verne'south description of gravitational effects is incorrect.
Solution:

Chapter 12 Gravity Q.23P
Consider an asteroid with a radius of 19 km and a mass of 3.35 10 1015 kg. Assume the asteroid is roughly spherical, (a) What is the dispatch due to gravity on the surface of the asteroid? (b) Suppose the asteroid spins about an axis through its eye, like the Earth, with a rotational period T. What is the smallest value T tin have earlier loose rocks on the asteroid's equator brainstorm to wing off the surface?
Solution:

Affiliate 12 Gravity Q.24P
CE Predict/Explain The Speed of the World The orbital speed of the Earth is greatest around January 4 and least effectually July iv. (a) Is the distance from the Earth to the Sun on January four greater than, less than, or equal to its altitude from the Sun on July 4? (b) Cull the best explanation from among the following:
I. The Earth's orbit is round, with equal distance from, the Lord's day at all times.
2. The Earth sweeps out equal area in equal time, thus it must be closer to the Sun when information technology is moving faster.
III. The greater the speed of the Globe, the greater its distance from the Sun.
Solution:
a) The distance from the Earth to the Sun on Jan 4, is less than the distance from the Sun on July 4.
b) The World sweeps out equal surface area in equal time, thus it must be closer to the sun when information technology is moving faster.

Chapter 12 Gravity Q.25P
C E A satellite orbits the Earth in a circular orbit of radius r. At some indicate its rocket engine is fired in such a way that its speed increases rapidly by a modest amount. As a result, do the (a) apogee distance and (b) perigee distance increase, subtract, or stay the same?
Solution:
Employ the concept of orbital transfer to identify the satellite into a new orbit.
(a)
The decelerating or accelerating rockets at some point in the circular orbit of the satellite would allow the satellite into a new orbit which is not a circle. The new orbit is an ellipse. The largest distance between the Earth and the satellite in an elliptical orbit is called the apogee distance. In the case of transfer of orbits, the apogee distance increases if the speed of the rocket increases a while in the original orbit.
(b)
The smallest distance between the World and the satellite in an elliptical orbit is nix simply the perigee altitude. In case of transfer of orbits, the perigee distance doesn't modify and equal to the radius of the original round orbit.

Chapter 12 Gravity Q.26P
g Repeat the previous problem., only this fourth dimension with the rocket engine of the satellite fired in such a way every bit to irksome the satellite.
Solution:
(A) The satellite drops into an elliptical orbit that brings it closer to Earth.
(B) The apogee distance remains unchanged.
(C) The perigee distance is reduced.

Affiliate 12 Gravity Q.27P
CE Predict/Explain The Earth-Moon Distance Is Increasing Laser reflectors left on the surface of the Moon by the Apollo astronauts evidence that the average distance from the Earth to the Moon is increasing at the rate of 3.8 cm per year. (a) Every bit a upshot, will the length of the calendar month increase, decrease, or remain the same? (b) Choose the all-time expianation from among the following: I. The greater the radius of an orbit, the greater the menses,
which implies a longer calendar month.
2. The length of the calendar month volition remain the same due to conservation of angular momentum,
Iii. The speed of the Moon is greater with increasing radius; therefore, the length of the month volition be less.
Solution:
a) If the average distance increases, then the length of the calendar month also increases.
b) The period depends upon the radius. Greater the radius, greater will be the menstruum. Pick (1) is correct.

Chapter 12 Gravity Q.28P
Apollo Missions On Apollq missions to the Moon, the command module orbited at an distance of 110 km above the lunar surface. How long did it accept for the command module to complete one orbit?
Solution:

Chapter 12 Gravity Q.29P
Observe the orbital speed of a satellite in a geosynchronous circular orbit three.58 X 107 g above the surface of the Earth.
Solution:

Chapter 12 Gravity Q.30P
An Extrasolar Planet In July of 1999 a planet was reported to exist orbiting the Dominicus-like star Iota Horologii with a period of 320 days. Observe the radius of the planet's orbi t, bold that iota Horologii has the same mass as the Sun. (This planet is presumably similar to Jupiter, simply information technology may have big, rocky moons that bask a relatively pleasant climate.)
Solution:

Chapter 12 Gravity Q.31P
Phobos, one of the moons of Mars, orbits at a altitude of 9378 km from the heart of the ruby-red planet. What is the orbital flow of Phobos?
Solution:

Affiliate 12 Gravity Q.32P
· The largest moon in the solar organisation is Ganymede, a moon of Jupiter. Ganymede orbits at a distance of one.07 10 109 k from the eye of Jupiter with an orbital menstruum of near six.eighteen X x′ s. Using this information, detect the mass of Jupiter.
Solution:

Chapter 12 Gravity Q.33P
IP Am Asteroid with Its Own Moon The asteroid 243 Ida has its ain modest moon, Dactyl. (Meet the photo on p. 390) (a) Outline a strategy to detect the mass of 243 Ida, given that the orbital radius of Dactyl is 89 km arid its period is 19 hour. (b) Use your strategy to calculate the mass of 243 Ida.
Solution:

Affiliate 12 Gravity Q.34P
GPS Satellites GPS (Global Positioning Organization) satellites orbit at an distance of ii.0 x 107 m. Observe (a) the orbital period, and (b) the orbital speed of such a satellite.
Solution:

Chapter 12 Gravity Q.35P
IP Two satellites orbit the Earth, with satellite 1 at a greater altitude than satellite 2. (a) Which satellite has the greater orbital speed? Explain, (b) Calculate the orbital speed of a satellite that orbits at an altitude of one Earth radius above the surface of the Earth, (c) Summate the orbital speed of a satellite that orbits at an altitude of two Earth radii above the surface of the Globe.
Solution:

Chapter 12 Gravity Q.36P
IP Calculate the orbital periods of satellites that orbit (a) one Earth radius above the surface of the Globe and (b) two Earth radii above the surface of the Globe, (c) How do your answers to parts (a) and (b) depend on the mass of the satellites? Explain, (d) How do your answers to parts (a) and (b) depend on the mass of the Earth? Explicate.
Solution:

Affiliate 12 Gravity Q.37P
South P The Martian moon Deimos has an orbital period that is greater than the other Martian moon, Phobos. Both moons take approximately circular orbits, (a) Is Deimos closer to or further from Mars than Phobos? Explain, (b) Calculate the distance from the center of Mars to Deimos given that its orbital menses is one.10 × 105 s.
Solution:

Chapter 12 Gravity Q.38P
Binary Stars Centauri A and Centauri B are binary stars with a separation of three.45 × 1012 m and an orbital flow of two.52 × 109 s. Assuming the two stars are equally massive (which is approximately the case), determine their mass.
Solution:

Chapter 12 Gravity Q.39P
Discover the speed of Centauri A and Centauri B, using the data given in the previous problem.
Solution:

Chapter 12 Gravity Q.40P
Sputnik The first bogus satellite to orbit the Earth was Sputnik I, Saunched October 4,1957. The mass of Sputnik 1 was 83.5 kg, and its distances from the center of the Globe at apogee and perigee were 7330 km-and 6610 km, respectively. Discover the deviation in gravitational potential energy for Sputnik I equally it moved from apogee to perigee.
Solution:

Chapter 12 Gravity Q.41P
CE Predict/Explain (a) Is the corporeality of energy required to get a spacecraft from the World to the Moon greater than, less than, or equal to the free energy required to get the same spacecraft from the Moon to the Globe? (b) Choose the all-time explanation from among the following:
I. The escape speed of the Moon is less than that of the World; therefore, less energy is required to go out the Moon.
2. The situation is symmetric, and hence the same amount of energy is required to travel in either direction.
Iii. It takes more free energy to go from the Moon to the Earth considering the Moon is orbiting the Earth.
Solution:
Use the concept of escape speed of the planet. The escape speed of the planet is the minimum speed at which the object frees from the gravitational attraction of the planet.
(a)
The escape speed of an object launched from the planet depends just on the mass and size of the planet, simply not on the mass of the object. The escape speed of the Globe is much greater than that of the Moon. Since the kinetic free energy is directly proportional to the square of the velocity, the more energy is required to launch the spacecraft from the Earth to the Moon than that required to launch the spacecraft from the Moon to the Earth.
(b)
The option (I) is correct.

Chapter 12 Gravity Q.42P

Solution:

Chapter 12 Gravity Q.43P
Calculate the gravitational potential energy of a 8.8-kg mass (a) on the surface of the Earth and (b) at an altitude of 350 km. (c) Take the deviation betwixt the results for parts (b) and (a), and compare with nigh, where h = 350 km.
Solution:

Chapter 12 Gravity Q.44P
2 0.59-kg basketballs, each with a radius of 12 cm, are simply touching. How much energy is required to change the separation between the centers of the basketballs to (a) i.0 m and (b) 10.0 k? (Ignore any other gravitational interactions.)
Solution:

Chapter 12 Gravity Q.45P
Find the minimum kinetic energy needed for a 39,000-kg rocket to escape (a) the Moon or (b) the Earth.
Solution:

Affiliate 12 Gravity Q.46P
CE Predict/Explicate Suppose the Earth were to suddenly shrink to half its current diameter, with its mass remaining constant, (a) Would the escape speed of the Earth increase, decrease, or stay the aforementioned? (b) Cull the best explanation from among the following:
I. Since the radius of the Earth would be smaller, the escape speed would as well be smaller.
Ii. The World would have the same amount of mass, and hence its escape speed would exist unchanged.
III. The force of gravity would exist much stronger on the surface of the compressed Earth, leading to a greater escape speed.
Solution:
a) The escape speed of the earth increases.
b) The strength of gravity would be much stronger on the surface of compressed Globe, leading to a greater escape speed. Option (Iii) is correct.

Chapter 12 Gravity Q.47P
CE Is the free energy required to launch a rocket vertically to a elevation h greater than, less than, or equal to the free energy required to prit the same rocket into orbit at the height hi Explicate.
Solution:
The energy required to launch a rocket vertically to a height h is equal to the potential energy of the rocket at that height. However, for a rocket to be put into orbit at a height h, both kinetic energy and potential energy are required. So the energy required for the rocket to be put into orbit is greater than the free energy required to launch a rocket vertically to the aforementioned meridian.

Chapter 12 Gravity Q.48P
Suppose 1 of the Global Positioning Arrangement satellites has a speed of 4.46 km/s at perigee and a speed of 3.64 km/s at apogee. If the distance from the eye of the Earth to the satellite at perigee is two.00 × 104 lem, what is the corresponding distance at apogee?
Solution:

Chapter 12 Gravity Q.49P

Solution:

Chapter 12 Gravity Q.50P
· Referring to Example 12-1, if the Millennium Eagle is at rest at point A, what is its speed at point B?
Solution:

Chapter 12 Gravity Q.51P
What is the launch speed of a projectile that rises vertically in a higher place the Earth to an distance equal to one Globe radius before coming to residuum momentarily?
Solution:

Chapter 12 Gravity Q.52P
A projectile launched vertically from the surface of the Moon? rises to an altitude of 365 km. What was the projectile's initial speed?
Solution:

Affiliate 12 Gravity Q.53P
Find the escape velocity for (a) Mercury and (b) Ventis.
Solution:

Affiliate 12 Gravity Q.54P
IP Halley's Comet Halley'south comet, which passes around the Sun every 76 years, has an elliptical orbit. When closest to the Sun (perihelion) information technology is at a distance of viii.823 10 1010 m and moves with a speed of 54.6 km/due south. The greatest distance between Halley's comet and the Sunday (aphelion) is 6.152 x 1012 1000. (a) Is the speed of Halley's comet greater than or less than 54.6 km/southward when information technology is at aphelion? Explain, (b) Calculate its speed ai aphelion.
Solution:

Chapter 12 Gravity Q.55P
The End of the Lunar Module On Apollo Moon missions, the lunar module would boom off from the Moon'southward surface and dock with the command module in lunar orbit. Subsequently docking, the lunar module would be jettisoned and allowed to crash back onto the lunar surface. Seismometers placed on the Moon's surface past the astronauts would and so selection up the resulting seismic waves. Find the bear upon speed of the lunar module, given that it is jettisoned from an orbit 110 km above the lunar surface moving with a speed of 1630 yard/s.
Solution:

Chapter 12 Gravity Q.56P
If a projectile is launched vertically from the Earth with a speed equal to the escape speed, how high above the Globe's surface is information technology when its speed is half the escape speed?
Solution:

Chapter 12 Gravity Q.57P
Suppose a planet is discovered orbiting a afar star. If the mass of the planet is 10 times the mass of the World, and its radius is one-tenth the Earth'due south radius, how does the escape speed of this planet compare with that of the Earth?
Solution:

Chapter 12 Gravity Q.58P
A projectile is launched vertically from the surface of the Moon with an initiaL speed of 1050 one thousand/south. At what altitude is the projectile's speed half its initial value?
Solution:

Chapter 12 Gravity Q.59P
To what radius would the Sun have to exist contracted for its escape speed to equal the speed of light? (Black holes have escape speeds greater than the speed of light; hence we see no calorie-free from them.)
Solution:

Chapter 12 Gravity Q.60P
IP Two baseballs, each with a mass of 0.148 kg, are separated by a distance of 395 m in outer infinite, far from any other objects. (a) If the assurance are released from rest, what speed do they take when their separation has decreased to 145 g? (b) Suppose the mass of the balls is doubled. Would the speed found in part (a) increase, decrease, or stay the same? Explicate.
Solution:

Chapter 12 Gravity Q.61P
On Earth, a person can jump vertically and ascension to a pinnacle h. What is the radius of the largest spherical asteroid from which this person could escape by jumping straight upward? Assume that each cubic meter of the asteroid has a mass of 3500 kg.
Solution:

Affiliate 12 Gravity Q.62P
As will be shown in Problem 63, the magnitude of the tidal force exerted on an object of mass thousand and length a is approximately 4GmMa/r3. In this expression, Thou is the mass of the torso causing the tidal force and r is the distance from the center of 1000 to the center of M. Suppose you are 1 1000000 miles away from a blackness hole whose mass is a 1000000 times that of the Sun. (a) Estimate the tidal force exerted on your body by the black hole. (b) At what distance volition the tidal strength be approximately 10 times greater than your weight?
Solution:

Chapter 12 Gravity Q.63P

Solution:

Chapter 12 Gravity Q.64P

Solution:

Chapter 12 Gravity Q.65GP
CE Y'all weigh yourself on a scale inside an airplane flying due east to a higher place the equator. If the airplane now turns around and heads due west with the same speed, will the reading on the calibration increment, decrease, or stay the same? Explain.
Solution:
SOLUTION:
The reading on the calibration is due to the force of gravity betwixt the person on the plane and the Earth.
F = Gm1m2 / R2
Where R is the divergence between the passenger on the plane and the center of the Globe. As the plane switches management from East to Westward, the R value remains unchanged. Since the mass of the person and the mass of the Earth are both the aforementioned, the magnitude of gravitational forcefulness will be the same.

Affiliate 12 Gravity Q.66GP

Solution:

Affiliate 12 Gravity Q.67GP

Solution:



Thus the increasing order of gravitational force is given by
object C >object A >object B

Affiliate 12 Gravity Q.68GP

Solution:

Chapter 12 Gravity Q.69GP
CE A satellite goes through one complete orbit of the Earth. (a) Is the cyberspace work done on it by the Earth's gravitational force positive, negative, or goose egg? Explain, (b) Does your answer to office (a) depend on whether the orbit is circular or elliptical?
Solution:
(A) When a satellite goes through one complete orbit, this means the satellite returns to
the initial point at which information technology started. The resulting net displacement is cipher. So the cyberspace piece of work done on information technology by Earth's gravitational force is zero.
(B) No, the respond to function (A) is independent of the shape of the orbit (i.e., whether the orbit is circular or elliptical). It is dependent on the displacement by the satellite.

Affiliate 12 Gravity Q.70GP
CE The Crash of Skylab Skylab, the largest spacecraft ever to fall back to the Earth, met its fiery terminate on July xi,1979, after flight directly over Everett, WA, on its last orbit. On the CBS Evening News the night before the crash, anchorman Walter Cronkite, in his rich baritone voice, made the post-obit statement: "NASA says there is a little chance that Skylab will country in a populated surface area." After the commercial, he immediately corrected himself by maxim,"I meant to say 'in that location is little risk' Skylab will hita populated area." In fact, it landed primarily in the Indian Sea off the west declension of Commonwealth of australia, though several pieces were recovered near the boondocks of Espérance, Australia, which later sent the U.Due south. State Section a $400 nib for littering. The cause of Skylab'due south crash was the friction it experienced in the upper reaches of the Earth's atmosphere. Every bit the radius of Skylab's orbit decreased, did its speed increase, decrease, or stay the aforementioned? Explicate.
Solution:
The speed of the Skylab increases with decreasing radius. We might call back that friction would slow Skylab but similar other objects are slowed by friction – but past dropping Skylab to a lower orbit, friction is ultimately responsible for an increment in speed.

Chapter 12 Gravity Q.71GP
Consider a system consisting of iii masses on the 10 centrality. Mass m1 = one.00 kg is at 10 = one.00 yard; mass m2 = 2.00 kg is at x = 2.00 1000; and mass m3 = 3.00 kg is at ten = 3.00 m. What is the total gravitational potential free energy of this system?
Solution:

Chapter 12 Gravity Q.72GP
An astronaut exploring a afar solar organization lands on an unnamed planet with a radius of 3860 km. When the astronaut jumps upward with an initial speed of three.10 chiliad/south, she rises to a pinnacle of 0.580 m. What is the mass of the planet?
Solution:

Affiliate 12 Gravity Q.73GP
IP When the Moon is in its third-quarter phase, the Earth, Moon, and Sun class a correct triangle, as shown in Figure 12-22. Summate the magnitude of the forcefulness exerted on the Moon by (a) the World and (b) the Dominicus. (c) Does it make more sense to think of the Moon as orbiting the Sun, with a pocket-sized effect due to the Earth, or as orbiting the Earth, with a small-scale event due to the Dominicus?
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Chapter 12 Gravity Q.74GP

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Chapter 12 Gravity Q.75GP

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Chapter 12 Gravity Q.76GP
A Most Miss! In the early forenoon hours of June 14, 2002, the World had a remarkably close encounter with an asteroid the size of a small city. The previously unknown asteroid, now designated 2002 MN, remained undetected until 3 days after it had passed the Earth. At its closest approach, the asteroid was 73,600 miles from the center of the Earth?nearly a third of the distance to the Moon. (a) Find the speed of the asteroid at closest arroyo, bold its speed at infinite distance to be cipher and considering but its interaction with the Barth. (b) Observations indica te the asteroid to have a diameter of about ii.0 km. Judge the kinetic energy of the asteroid at closest approach, assuming it has an average density of 3.33 one thousand/cm3 (For comparison, a 1-megaton nuclear weapon releases about 5.six × 1015J of energy.)
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Chapter 12 Gravity Q.77GP
IP Suppose a planet is discovered that has the same amount of mass in a given volume as the Earth, merely has half its radius. (a) Is the acceleration due to gravity on this planet more than, less than, or the same as the dispatch due to gravity on the World? Explain. (b) Summate the acceleration due to gravity on this planet.
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Affiliate 12 Gravity Q.78GP
IP Suppose a planet is discovered that has the same total mass as the Globe, but half its radius. (a) Is the acceleration due to gravity on this planet more than than, less than, or the same as the dispatch due to gravity on the Earth? Explicate. (b) Calculate the acceleration due to gravity on this planet.
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Chapter 12 Gravity Q.79GP

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Chapter 12 Gravity Q.80GP

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Affiliate 12 Gravity Q.81GP

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Affiliate 12 Gravity Q.82GP
Using the results from Problem 54. observe the angular momentum of Halley's comet (a) at perihelion and (b) at aphelion (Take the mass of Halley's comet to be ix.8 10 1014 kg.)
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Chapter 12 Gravity Q.83GP
Exploring Mars Inthe not-too-distant future astronauts will travel to Mars to comport out scientific explorations. As part of their mission, it is probable that a "geosynchronous" satellite volition exist placed above a given signal on the Martian equator to facilitate communications. At what altitude above the surface of Mars should such a satellite orbit? (Note: The Martian "day" is 24.6229 hours, Other relevant information can be found in Appendix C.)
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Chapter 12 Gravity Q.84GP
IP A satellite is placed in Earth orbit 1000 miles college than the distance of a geosynchronous satellite. Referringto Active Example 12-ane, we see that the altitude of the satellite is 23,300 mi. (a) Is the catamenia of this satellite greater than or less than 24 hours? (b) As viewed from the surface of the World, does the satellite move eastward or westward? Explain. (c) Find the orbital period of this satellite.
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Chapter 12 Gravity Q.85GP
Find the speed of the Millennium Hawkeye at point A in Example 12-1 if its speed at point B is 0.905 m/southward.
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Chapter 12 Gravity Q.86GP
Show that the force of gravity between the Moon and the Sun is e'er greater than the strength of gravity betwixt the Moon and the Earth.
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Chapter 12 Gravity Q.87GP

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Affiliate 12 Gravity Q.88GP
(a) Find the kinetic energy of a 1720-kg satellite in a circular orbit about the Earth, given that the radius of the orbit is 12,600 miles. (b) How much energy is required to move this satellite to a circular orbit with a radius of 25,200 miles?
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Chapter 12 Gravity Q.89GP
IP Space Shuttle Orbit On a typical mission, the space shuttle (grand = 2.00 × 106 kg) orbits at an altitude of 250 km above the Earth's surface. (a) Does the orbital speed of the shuttle depend on its mass? Explicate. (b) Find the speed of the shuttle in its orbit. (c) How long does it take for the shuttle to consummate one orbit of the Earth?
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Chapter 12 Gravity Q.90GP
IP Consider an object of mass m orbiting the Globe at a radius r. (a) Find the speed of the object. (b) Show that the total mechanical energy of this object is equal to (?1) times its kinetic free energy. (c) Does the result of part (b) apply to an object orbiting the Sun? Explain.
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Chapter 12 Gravity Q.91GP
In a binary star system two stars orbit about their common center of mass. Find the orbital menses of such a system, given that the stars are separated by a distance d and accept masses grand and 2m.
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Chapter 12 Gravity Q.92GP

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Affiliate 12 Gravity Q.93GP
Discover an expression for the kinetic energy of a satellite of mass yard in an orbit of radius r about a planet of mass K.
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Chapter 12 Gravity Q.94GP
Referring to Instance 12-1, find the ten component of the net force acting on the Millennium Eagle as a function of 10. Plot your outcome, showing both negative and positive values of x.
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Chapter 12 Gravity Q.95GP
A satellite orbits the Earth in an elliptical orbit. At perigee its distance from the center of the Earth is 22,500 km and its speed is 4280 m/s. At apogee its distance from the center of the Earth is 24,100 km and its speed is 3990 1000/south. Using this information, calculate the mass of the Earth.
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Affiliate 12 Gravity Q.96PP

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Chapter 12 Gravity Q.97PP

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Chapter 12 Gravity Q.98PP

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Chapter 12 Gravity Q.99PP

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Chapter 12 Gravity Q.100IP
Notice the orbital radius that corresponds to a "year" of 150 days.
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Chapter 12 Gravity Q.101IP
Suppose the mass of the Dominicus is suddenly doubled, just the World's orbital radius remains the aforementioned. (a) Would the length of an Earth yr increase, decrease, or stay the aforementioned? (b) Notice the length of a yr for the case of a Lord's day with twice the mass. (c) Suppose the Sun retains its present mass, simply the mass of the Earth is doubled instead. Would the length of the year increase, decrease, or stay the same?
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Chapter 12 Gravity Q.102IP
(a) If the mass of the Earth were doubled, would the escape speed of a rocket increment, subtract, or stay the same? (b) Calculate the escape speed of a rocket for the instance of an World with twice its nowadays mass. (c) If the mass of the Globe retains its present value, but the mass of the rocket is doubled, does the escape speed increase, decrease, or stay the same?
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The escape speed depends on the mass of Earth, radius of Earth, and the universal gravitational abiding. Nevertheless, it does not depend on the mass of the rocket.

Chapter 12 Gravity Q.103IP
Suppose the Earth is all of a sudden shrunk to half its nowadays radius without losing any of its mass. (a) Would the escape speed of a rocket increment, subtract, or stay the aforementioned? (b) Find the escape speed for an Earth with half its nowadays radius.
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