Given the perihelion distance, p, and aphelion distance, q, for an elliptical orbit, show that the velocity at perihelion, v p , is given by v p = √((2GMSun /(q + p)) . (q/p)) . (Hint: Use conservation of angular momentum to relate v p and vq , and then substitute into the conservation of energy equation.)
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Given the perihelion distance, p, and aphelion distance, q, for an elliptical orbit, show that the velocity at perihelion, v p , is given by v p = √((2GMSun /(q + p)) . (q/p)) . (Hint: Use conservation of
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- Help me with the complete solution for question number 9.24 . as well as the given and required correct answer provided.I am given an equation (attatched image) and am told that G = newtons gravitational constant, m1 is the mass of the first object, m2 is the mass of the second object, and r is the distance separating them. Consider m1 to be stationary with m2 undergoing uniform circular motion around m1 at a distance r. How do I show that GPE = -2KE for any gravitational circular orbit (where KE is the kinetic energy of object 2).Let’s imagine that you have an idea for an experiment to fly on NASA’s “Vomit Comet.” (What’s special about this plane? It flies in parabolic paths (aka freefall) which result in near weightlessness. This means that you can ignore the effects of gravity when plan your experiment.) You want to mimic the orbital motion of the planets but by using electrostatic force rather than gravitational. And, instead of a planet, you will be orbiting a droplet of water that is 0.5mm in radius and has an deficit of 1.5 x 106 electrons. The droplet is to orbit around a small (1cm radius) sphere. If you want the droplet to move with an orbital radius of 14cm and period of one minute, what should the charge be on the central sphere? BTW The density of water is 997 kg/m3.
- How much energy is required to move a satellite of mass 1000 kg from the surface of the Earth to an altitude 3 times the radius of the Earth? Compute the energy in joules.Plaskett's binary system consists of two stars that revolve in a circular orbit about a center of mass midway between them. This statement implies that the masses of the two stars are equal (see figure below). Assume the orbital speed of each star is |v| 190 km/s and the orbital period of each is 12.9 days. Find the mass M of each star. (For comparison, the mass of our Sun is 1.99 x 1030 kg.) solar masses M XCM MA spacecraft traveling at a velocity of (-20, -90, 40) m/s is observed to be at a location (200, 300, -500) m relative to an origin located on a nearby asteroid. At a later time, the spacecraft is at location (-380, −2310, 660) m. (a) How long did it take the spacecraft to travel between these locations? (b) How far did the spacecraft travel? (c) What is the speed of the spacecraft (d) What is the unit vector in the direction of the spacecraft's velocity?
- 3. Let's imagine that the earth is shrinking and we want to escape before it is too late. Let's set up some notation: R: the radius of Earth MẸ : the mass of Earth m: your mass G : the universal gravitational constant c: the speed of light Note that, since Earth is shrinking, R is not constant, but MẸ is constant (the values of ME, G and c are available on Wikipedia). In this question, we will compute the velocity needed to escape Earth and the radius of (shrunken) Earth for which even light cannot escape (when Earth becomes a black hole). In fact, all of the related formulae are well known and the purpose of this question is to justify our work using what we have learned in this course so far. (a) The work (energy) W needed to free yourself from Earth when its radius is R metres is w = G ME m dh. h2 R Show that this improper integral is equal to GME m RShow that the minimum energy required to launch a satellite of mass m from the surface of the earth in a circular orbit at an altitude h = R, where R is the 3mgR where M is the mass of 4 radius of the earth is the earth.