Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
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Chapter 8, Problem 64P
To determine
The orbit of the two asteroids.
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The Rosetta mission was the first one to land a spacecraft on a comet, specifically
comet 67P/Churyumov-Gerasimenko. 67P has a semi major axis a = 3.4630 AU
with an eccentricity e = 0.64102.
67P
Sun
a
a) What is the velocity of 67P at the aphelion (point of maximum distance to the
Sun)?
b) What is the total mechanical energy of this comet?
c) What is its velocity at the perihelion (point of minimum distance to the Sun)?
d) What is the velocity of 67P at a distance r = 4.1283 AU from the Sun?
e) What is the orbital period of 67P? (For this question you may assume a
circular orbit with radius equal to a)
DATA:
Nm2
G = 6.6725 x 10-11
kg2
M67P = 9.982 x 1012 kg
Msun = 1.989 x 1030 kg
1 AU = 1.495978707 x 101 m
A 0.872 km diameter asteroid will make a crater about 10 km in diameter. Let the asteroid have a density of 3000 kg/m3 and impact the surface at 22 km/sec. Assuming a spherical asteroid, what is the kinetic energy (in joule) of the asteroid? Convert the answer to megatons of TNT, where 1 megaton is about 4 × 1015 joule. For comparison, the most energetic weapon in the human arsenal is about 100 megatons.
A 1 kg satellite is to be placed at 3.55e7 meters above the earth's surface. What is the difference in potential energy between Earth's surface and the satellite height for a satellite with 1 kg mass? What is the total work needed to place the satellite in orbit at this location above earth?
Chapter 8 Solutions
Essential University Physics (3rd Edition)
Ch. 8.2 - Suppose the distance between two objects is cut in...Ch. 8.3 - Suppose the paths in Fig. 8.8 are the paths of...Ch. 8.4 - Prob. 8.3GICh. 8 - What do Newtons apple and the Moon have in common?Ch. 8 - Prob. 2FTDCh. 8 - When you stand on Earth, the distance between you...Ch. 8 - The force of gravity on an object is proportional...Ch. 8 - A friend who knows nothing about physics asks what...Ch. 8 - Could you put a satellite in an orbit that keeps...Ch. 8 - Why are satellites generally launched eastward and...
Ch. 8 - Given Earths mass, the Moons distance and orbital...Ch. 8 - How should a satellite be launched so that its...Ch. 8 - Does the gravitational force of the Sun do work on...Ch. 8 - Space explorers land on a planet with the same...Ch. 8 - Use data for the Moons orbit from Appendix E to...Ch. 8 - Prob. 13ECh. 8 - Prob. 14ECh. 8 - Two identical lead spheres with their centers 14...Ch. 8 - Whats the approximate value of the gravitational...Ch. 8 - A sensitive gravimeter is carried to the top of...Ch. 8 - Prob. 18ECh. 8 - Find the speed of a satellite in geostationary...Ch. 8 - Marss orbit has a diameter 1.52 times that of...Ch. 8 - Calculate the orbital period for Jupiters moon Io,...Ch. 8 - An astronaut hits a golf ball horizontally from...Ch. 8 - The Mars Reconnaissance Orbiter circles the red...Ch. 8 - Earths distance from the Sun varies from 147 Gm at...Ch. 8 - Prob. 25ECh. 8 - A rocket is launched vertically upward from Earths...Ch. 8 - What vertical launch speed is necessary to get a...Ch. 8 - Find the energy necessary to put 1 kg, initially...Ch. 8 - Whats the total mechanical energy associated with...Ch. 8 - Prob. 30ECh. 8 - Determine escape speeds from (a) Jupiters moon...Ch. 8 - Prob. 32ECh. 8 - The gravitational acceleration at a planets...Ch. 8 - One of the longest-standing athletic records is...Ch. 8 - Prob. 35PCh. 8 - If youre standing on the ground 15 m directly...Ch. 8 - Given the Moons orbital radius of 384,400 km and...Ch. 8 - Equation 7.9 relates force to the derivative of...Ch. 8 - During the Apollo Moon landings, one astronaut...Ch. 8 - Prob. 40PCh. 8 - Prob. 41PCh. 8 - Youre preparing an exhibit for the Golf Hall of...Ch. 8 - Prob. 43PCh. 8 - Satellites A and B are in circular orbits, with A...Ch. 8 - The asteroid that exploded over Chelyabinsk,...Ch. 8 - Prob. 46PCh. 8 - Prob. 47PCh. 8 - Neglecting air resistance, to what height would...Ch. 8 - Show that an object released from rest very far...Ch. 8 - Prob. 50PCh. 8 - Prob. 51PCh. 8 - Prob. 52PCh. 8 - Prob. 53PCh. 8 - Prob. 54PCh. 8 - Prob. 55PCh. 8 - Two meteoroids are 160,000 km from Earths center...Ch. 8 - Two rockets are launched from Earths surface, one...Ch. 8 - Prob. 58PCh. 8 - A missiles trajectory takes it to a maximum...Ch. 8 - Prob. 60PCh. 8 - Mercurys orbital speed varies from 38.8 km/s at...Ch. 8 - Prob. 62PCh. 8 - Two satellites are in geostationary orbit but in...Ch. 8 - Prob. 64PCh. 8 - Prob. 65PCh. 8 - We derived Equation 8.4 on the assumption that the...Ch. 8 - Prob. 67PCh. 8 - As a member of the 2040 Olympic committee, youre...Ch. 8 - The Olympic Committee is keeping you busy! Youre...Ch. 8 - Tidal forces are proportional to the variation in...Ch. 8 - Spacecraft that study the Sun are often placed at...Ch. 8 - Prob. 72PPCh. 8 - Prob. 73PPCh. 8 - Prob. 74PPCh. 8 - The Global Positioning System (GPS) uses a...
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- Find an expression for the square of the orbital period. Express your answer in terms of G, M, R, and π. The potential energy U of an object of mass m that is separated by a distance R from an object of mass M is given by U=−G*Mm/R. What is the kinetic energy K of the satellite? Express your answer in terms of the potential energy U.arrow_forwardTwo spherical asteroids have the same radius R. Asteroid 1 has mass M and asteroid 2 has mass 2M. The two asteroids are released from rest with distance 10R between their centers. What is the speed of each asteroid just before they collide? Hint: You will need to use two conservation laws.arrow_forwardA space probe is in orbit around Mars at an altitude of 1200 km. To move to a higher orbit, small rocket engines are used to provide the energy required.(a) Compare the kinetic energy of the space probe in the lower and higher orbit.(b) Explain why energy is required to move the space probe from a lower to a higher orbit. In your answer refer to the total energy of the satellite.arrow_forward
- Two Martian satellites, A and B, are in circular orbits around Mars’ center. Satellite A orbits at an altitude of 4200 km, and satellite B orbits at an altitude of 12,600 km. The mass of each satellite is 950kg. a. What are the potential energies of the two satellites? (Note, altitude is measured from the surface of a planet, but the distances in the expressions for force/energy/field are measured from the center of the planet.) b.What are the kinetic energies of the two satellites? c. How much work would be required to move satellite A to the orbit of satellite B?arrow_forwardanswer 3(a)arrow_forwardIn the past, asteroids striking the earth have produced disastrous results. If we discovered an asteroid on a collision course with the earth, we could, in principle, deflect it and avoid an impact by focusing a laser on the surface. Intense surface heating from the laser could cause surface material to be ejected into space at high speed. How would this deflect the asteroid?arrow_forward
- Using the above equation and what you know about kinetic energy and energy conservation, show that the expression for the escape velocity ve from a planet of radius R is . (Hint: To just escape the planet, the object’s speed must be 0 infinitely far from the planet.) and find the escape velocity of an object being launched from Earth. Earth has a radius of and a mass of .arrow_forwardThe figure below shows the potential energy function U(r) of a projectile plotted outward from the surface of a planet of radius Rs. What is the minimum velocity required for a 1.8 kg object to "escape" the gravitational field of the planet.arrow_forwardAn asteroid closely passes the Earth at a range of 17200mi and a relative speed of 7.8km/s.The diameter is estimated at 30mwith a specific gravity of 3. If this asteroid had impacted Earth, how much energy would have been released? Express this quantity in units of mega-tons (M ton) where a megaton is the energy released by one million metric tons of TNT explosive. A metric ton is 1000kgand the explosive energy density of TNT is 4184J/g.Hint: If the asteroid hits the Earth, its relative velocity becomes zero. Ignore any change in asteroid velocity due to gravitational acceleration or air resistance.arrow_forward
- The International Space Station, which has a mass of 4.94×105 kg, orbits 258 miles above the Earth's surface, and completes one orbit every 94.3 minutes. What is the kinetic energy of the International Space Station in units of GJ (109 Joules)? (Note: don't forget to take into account the radius of the Earth!) Enter answer here GJarrow_forwardA meteor of mass m is approaching earth as shown on the sketch. The distance h on the sketch below is called the impact parameter. The radius of the earth is Re = 6400km . The 6x1024 kg mass of the earth is me = Suppose the meteor has an initial speed of vo = 30km/s. Assume that the meteor started very far away from the earth. Suppose the meteor just passes earth at a distance of 2.5Re from the earth's center. You may ignore all other gravitational forces except the earth. Find the moment arm h in km (called the impact parameter). G = 6.673x10-"Nm²kg 2 meteor very far away h impact parameter planetarrow_forwardAn asteroid closely passes the Earth at a range of 17200 mi and relative speed of 7.8 km/s. The diameter is estimated at 30 m with a specific gravity of 3. If this asteroid had impacted Earth, how much energy would have been released? Express this quantity in units of mega- tons (Mton) where a megaton is the energy released by one million metric tons of TNT explosive. A metric ton is 1000 kg and the explosive energy density of TNT is 4184 J/g. Hint: If the asteroid hits the Earth, its relative velocity becomes zero. Ignore any change in asteroid velocity due to gravitational acceleration or air resistance.arrow_forward
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