2. Three masses are placed on a plane such that the coordinates of the masses are, m1 = 1.0 kg at %3D (1,0), m2 = 2.0 kg at (2, 0), and m3 = 3.0 kg at (0, 3). %3D Determine the coordinates of the center of the mass of the three masses.
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- The sun is 333000 times as massive as earth, and they are a distance r apart. At what distance x from earth should an abject, half as massive as earth, be placed so it experiences zero gravitational pull due to the sun and earth? A. x= 1/2r B. x= 1/333000r C. x= 1/578r D. x= 1/3r E. x= 1/381rD mp M, Two planets orbit each other in stable circular orbits at a distance D = 7.06 × 10' km. The planets have masses m, 8.85 x 1024 kg and Mp 6.70 x 10º kg. The center of the lower mass planet, m,, is at the origin. How far along the line joining the two planets is the center of mass of the system? COM km Note: You can treat spherical bodies as point masses with all the mass at the center of the sphere. When solving this question, you can assume that all the mass m, is at the origin and all the mass Mp is a distance D away. Part 3) The planets both travel in circular orbits around this center of mass. Use this to calculate the speed of the lower mass planet, m,. Up m/s3. The asteroid belt between Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was destroyed). (a) If the center of mass of asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth, how long would it have taken this hypothetical planet to orbit the Sun? (b) Can we use these data to deduce the mass of this planet?
- Which of the following statements is correct regarding Kepler's three laws of planetary motion? Angular momentum of any planet about an axis through the Sun and perpendicular to the orbital plane is not invariant during its motion. Planets move in elliptical orbits with the sun not being at its center. O Orbital period of a planet is directly proportional to its distance from the sun. O Kepler's laws are valid only for planets in the solar system.Current Attempt in Progress Three dimensions. Three point particles are fixed in place in an xyz coordinate system. Particle A, at the origin, has mass ma. Particle B, at xyz coordinates (2.00d, 2.00d, 2.00d), has mass 4.00ma, and particle C, at coordinates (-3.00d, 2.00d, -3.00d), has mass 4.00mA. A fourth particle D, with mass 3.00ma, is to be placed near the other particles. If distance d = 4.20 m, at what (a) x, (b) y, and (c) z coordinate should D be placed so that the net gravitational force on A from B, C, and D is zero? %3D (a) Number i Units (b) Number Units (c) Number Units > >Two planets P₁ and P₂ orbit around a star S in circular orbits with speeds v₁ = 43.4 km/s, and v₂ = 57.0 km/s respectively. If the period of the first planet P₁ is 790 years what is the mass, in kg, of the star it orbits around? kg Determine the orbital period, in years, of P2. yr
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