C. Newton's law of universal gravitation states that two particles exert a pull on each other with magnitude F, ([kg · m/s']) that is proportional to the product of their masses mi ([kg]) and m: ([kg]) and inversely proportional to the square of their separation d ([m]). Write down an equation for Newton's law of universal gravitation and determine the Sl unit of all the proportionality constants you used.
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- 11) Newton's Law of Gravity says that the force of gravity between any two objects is G d2 where the m's are the masses of the objects and, d is the distance between them, and G is a constant that depends on your choice of units. This includes big things like planets and small things like you and your pets. We don't need to know the values of the masses to think about what happens as two objects approach each other! lim G d--0+ d? If you think too long about your answer, it may be a bit troubling. What does it say about the force of gravity when you actually touch your pets?2. Integrate the equations of motion for a spherical pendulum, i.e., a particle of mass m moving on the surface of a sphere of radius / in a gravitational field, with Lagrangian L = ml² -(0² + psin² 0) + mglcos 0. 2 Hint: Merely set up the integrals, do not evaluate them. You should obtain two integrals w.r.t. de: one determining t and another determining p. Express the first integral in terms of E,Ueff, m, and l. Express the second integral in terms of E,U eff, m, l, and M₂.Astronomers have observed a small, massive object at the center of our Milky Way Galaxy. A ring of material orbits this massive object; the ring has a diameter of about 17 light-years and an orbital speed of about 100 km/s. A) Determine the mass M of the massive object at the center of the Milky Way Galaxy. Give your answer in kilograms.Express your answer in kilograms. B) Give your answer in solar masses (one solar mass is the mass of the sun). Express your answer in units of solar masses. C) Many astronomers believe that the massive object at the center of the Milky Way Galaxy is a black hole. If so, what must the Schwarzschild radius RS of this black hole be? Express your answer in meters.
- how do i solve this problema. What is the difference between the force in F = ma (Newton's 2nd law) and F= Gm₁m₂/d² (Newton's law of universal gravitation). b. Find the net force on a Planet A of mass 3.0 x 101⁹ kg due to the gravitational attraction of both Planet B of mass 4.9 x 102⁰ kg and the Sun of mass 2.1 x 103⁰ kg, assuming they are at right angles to each other. The distance of Planet A from Planet B is 5.0 x 107 m and distance of the Sun from the Planet A is 5.8 x 106 m. G= 6.67 x 10-1¹ N.m²/kg². |Can I please get some help with the key concepts and principles, please and thank you!
- Tidal forces are gravitational forces exerted on different parts of a body by a second body. Their effects are particularly visible on the earth's surface in the form of tides. To understand the origin of tidal forces, consider the earth-moon system to consist of two spherical bodies, each with a spherical mass distribution. Let r. be the radius of the earth, m be the mass of the moon, and G be the gravitational constant. Part B Since the gravitational force between two bodies decreases with distance, the acceleration anear experienced by a unit mass located at the point on the earth's surface closest to the moon is slightly different from the acceleration afar experienced by a unit mass located at the point on the earth's surface farthest from the moon. Give a general expression for the quantity anear-afar Express your answer in terms of G, m, r, and re. ▸ View Available Hint(s) anear afar = ΜΕ ΑΣΦ ? x Xb √√x √x X [X] X.10" Variables are case sensitive. No credit lost. Try again.1. A force is given as Ẻ = xy² x + (x²y + y) ŷ. Calculate § F. dỉ along the circumference of a circle of radius 3.Part A The value of Gmdre", where me is the mass of the earth, r, is the radius of the earth, and G is the universal gravitational constant is (enter your answer with three significant figures) ΑΣΦ IXI X•10n -11 6.67 101 m/? Submit Previous Answers Request Answer X Incorrect; Try Again; 4 attempts remaining