교과서 질문
The dwarf planet Pluto has an elliptical orbit with a semimajor axis of 5.91 × 1012 m and eccentricity 0.249. During Pluto's orbit around the sun, what are its closest and farthest distances from the sun?
3031
views
Ch 13: Gravitation
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610
당신이 사용하는 게 아니라요?교과서 변경다른 교과서를 선택하세요
TOC.tableOfContents
- Ch 01: Units, Physical Quantities & Vectors41
- Ch 02: Motion Along a Straight Line67
- Ch 03: Motion in Two or Three Dimensions47
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws59
- Ch 06: Work & Kinetic Energy14
- Ch 07: Potential Energy & Conservation8
- Ch 08: Momentum, Impulse, and Collisions18
- Ch 09: Rotation of Rigid Bodies42
- Ch 10: Dynamics of Rotational Motion48
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics31
- Ch 13: Gravitation35
- Ch 14: Periodic Motion32
- Ch 15: Mechanical Waves25
- Ch 16: Sound & Hearing32
- Ch 17: Temperature and Heat36
- Ch 18: Thermal Properties of Matter38
- Ch 19: The First Law of Thermodynamics33
- Ch 20: The Second Law of Thermodynamics22
- Ch 21: Electric Charge and Electric Field36
- Ch 22: Gauss' Law24
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF26
- Ch 26: Direct-Current Circuits30
- Ch 27: Magnetic Field and Magnetic Forces18
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction28
- Ch 30: Inductance17
- Ch 31: Alternating Current21
- Ch 32: Electromagnetic Waves1
- Ch 33: The Nature and Propagation of Light20
- Ch 34: Geometric Optics34
- Ch 35: Interference19
- Ch 36: Diffraction25
- Ch 37: Special Relativity20
- Ch 38: Photons: Light Waves Behaving as Particles15
- Ch 39: Particles Behaving as Waves26
- Ch 40: Quantum Mechanics I: Wave Functions21
- Ch 41: Quantum Mechanics II: Atomic Structure25
- Ch 42: Molecules and Condensed Matter18
- Ch 43: Nuclear Physics16
- Ch 44: Particle Physics and Cosmology23
13장, 문제 27
The star Rho1 Cancri is 57 light-years from the earth and has a mass 0.85 times that of our sun. A planet has been detected in a circular orbit around Rho1 Cancri with an orbital radius equal to 0.11 times the radius of the earth's orbit around the sun. What are (a) the orbital speed and (b) the orbital period of the planet of Rho1 Cancri?
검증된 단계별 안내1
To find the orbital speed of the planet, we can use the formula for orbital speed: \( v = \sqrt{\frac{GM}{r}} \), where \( G \) is the gravitational constant, \( M \) is the mass of the star, and \( r \) is the orbital radius of the planet.
First, calculate the mass of Rho1 Cancri. Given that its mass is 0.85 times the mass of the sun, we have \( M = 0.85 \times M_{\text{sun}} \).
Next, determine the orbital radius \( r \) of the planet. It is given as 0.11 times the radius of Earth's orbit (1 astronomical unit, AU). Therefore, \( r = 0.11 \times 1 \text{ AU} \).
Substitute the values of \( G \), \( M \), and \( r \) into the orbital speed formula to find the speed \( v \).
To find the orbital period \( T \), use Kepler's third law: \( T^2 = \frac{4\pi^2r^3}{GM} \). Solve for \( T \) by substituting the known values of \( G \), \( M \), and \( r \).
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
4m도움이 되었나요?
주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Gravitational Force and Orbital Motion
Gravitational force is the attractive force between two masses, such as a star and a planet. It provides the necessary centripetal force to keep a planet in orbit. The balance between gravitational force and the planet's inertia determines the orbital speed and period, following Kepler's laws of planetary motion.
추천 영상:
가이드 코스
05:41
Gravitational Forces in 2D
Kepler's Third Law
Kepler's Third Law states that the square of a planet's orbital period is proportional to the cube of the semi-major axis of its orbit. This law helps relate the orbital period to the distance from the star, allowing us to calculate the period if the orbital radius and the star's mass are known.
추천 영상:
가이드 코스
08:32Kepler's Third Law
Circular Orbital Speed
The orbital speed of a planet in a circular orbit can be calculated using the formula v = √(GM/r), where G is the gravitational constant, M is the mass of the star, and r is the orbital radius. This formula derives from equating gravitational force to the centripetal force required for circular motion.
추천 영상:
가이드 코스
9:11Energy of Circular Orbits
관련 실천
교과서 질문
In 2004 astronomers reported the discovery of a large Jupiter-sized planet orbiting very close to the star HD 179949 (hence the term 'hot Jupiter'). The orbit was just 1/9 the distance of Mercury from our sun, and it takes the planet only 3.09 days to make one orbit (assumed to be circular). How fast (in km/s) is this planet moving?
2803
views
교과서 질문
In its orbit each day, the International Space Station makes 15.65 revolutions around the earth. Assuming a circular orbit, how high is this satellite above the surface of the earth?
3668
views
교과서 질문
Two satellites are in circular orbits around a planet that has radius 9.00 × 106 m. One satellite has mass 68.0 kg, orbital radius 7.00 × 107 m, and orbital speed 4800 m/s. The second satellite has mass 84.0 kg and orbital radius 3.00 × 107 m. What is the orbital speed of this second satellite?
3195
views
교과서 질문
On July 15, 2004, NASA launched the Aura spacecraft to study the earth's climate and atmosphere. This satellite was injected into an orbit 705 km above the earth's surface. Assume a circular orbit. How many hours does it take this satellite to make one orbit?
2708
views
교과서 질문
In March 2006, two small satellites were discovered orbiting Pluto, one at a distance of 48,000 km and the other at 64,000 km. Pluto already was known to have a large satellite Charon, orbiting at 19,600 km with an orbital period of 6.39 days. Assuming that the satellites do not affect each other, find the orbital periods of the two small satellites without using the mass of Pluto.
2108
views