Binary Star System A binary star system consists of two stars of masses mı and m2. The stars, which gravitationally attract each other, revolve around the center of mass of the system. The star with mass mi has a centripetal acceleration of magnitude aj. Part A Note that you do not need to understand universal gravitation to solve this problem. Find ag, the magnitude of the centripetal acceleration of the star with mass m2. Express the acceleration in terms of quantities given in the problem introduction. • View Available Hint(s) VO AE ? az =

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.

A satellite orbiting the earth is directly over a point on the equator at 12:00 midnight every two days. It is not over that point at any time in between. Part A What is the radius of the satellite's orbit? Express your answer with the appropriate units. C'H r = μA Value m ?

You are the pilot of a spacecraft intended for travel at very high speeds. Before leaving you measure the spacecraft to be 31.4 m long and have a mass of 5.28 x 104 kg. During your travel, you pass a planet and exchange information with an observer on the planet. You are told that your spacecraft has been measured to be 28.6 m long. a. How fast is your spacecraft travelling with respect to the planet? b. You are told there is a nearby planet that is stationary with respect to the first planet. The observer on the first planet says it will take you 25 s to reach the nearby planet. How far away does your co-pilot on the spacecraft say the nearby planet is? c. How much energy was required to accelerate your spacecraft to this speed?

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You are given two point-like objects, known as M1 & M2. M1 has four times the mass of M2 and they are placed at a distance of d apart from each other.  A. Can you sketch (in 2-dimensions) the gravitational field lines that are present in the region of space around the two masses. Show the direction of the field on the field lines.  B. Explain quantitatively where you should place a test particle such that it experiences a net gravitational force of zero from the two point-like objects. Indicated this position on your diagram.

A rocket with mass 7.00×103 kgkg is in a circular orbit of radius 7.50×106 mm around the earth. The rocket's engines fire for a period of time to increase that radius to 8.80×106 mm, with the orbit again circular.     Part A What is the change in the rocket's kinetic energy? Does the kinetic energy increase or decrease? Express your answer with the appropriate units. Enter positive value if the kinetic energy increases and negative value if the kinetic energy decreases.       ΔKΔK = nothingnothing   SubmitRequest Answer Part B What is the change in the rocket's gravitational potential energy? Does the potential energy increase or decrease? Express your answer with the appropriate units. Enter positive value if the gravitational potential energy increases and negative value if the gravitational potential energy decreases.       ΔUΔU = nothingnothing   SubmitRequest Answer Part C How much work…

Help with this would be great, thank you!

I've gone through like 4 pages trying to figure this out and i keep getting nonsensical answers.  Help would be greatly appreciated!