The masses Mi = 2M and M2 = M rotate around the mass M3 in cireular orbits shown in the figure. The relation between the forces acted on Mị and M2 by the mass M3 is given as F2= 8F1. a) Show the relationship between the orbital radii (R and r) of the masses M1 and M2. b) Show the relationship between the periods Ti and T2of the masses Mi and M2. c) Show the relation between the tangential velocities (V1 and V2) of the masses Mi and M2. R M M, Ma
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- Three uniform spheres of masses m₁ = 3.00 kg, m₂ = 4.00 kg, and m3 = 5.00 kg are placed at the corners of a right triangle (see figure below). Calculate the resultant gravitational force on the object of mass m₂, m2 assuming the spheres are isolated from the rest of the Universe. Î + × 10-11 N y (0, 3.00) m m (-4.00, 0) m 12 Mg F 32 Ο m2 xThe gas-giant planet Rom (mass 5.7⨯1026 kg) goes around the star Galla (mass 2.0⨯1030 kg) in a circular orbit at a speed of 9.7⨯103 m/s. Note: G = 6.67⨯10-11 N·m2/kg2 i) How far is it from Galla to Rom (from center to center)? ii) What is the period of Rom’s orbit in Earth years? (One Earth year is 365.25 Earth days.) iii) What is the magnitude of the force on Rom due to the Galla?The earth orbits the sun at an approximate velocity v = 30 km/s and radius r = 150*10^6 km. (a) Assuming a circular orbit for the earth, what is the approximate mass of the sun? (b) If the mass of the sun was doubled, what would the new length of a year be? Assume the Earth remains in circular orbit about the sun at its usual orbital radius. Answer in terms of current years. (Hint: you do not need to plug in the value of G.)
- Hunting a black hole. Observations of the light from a certain star indicate that it is part of a binary (two-star) system. This visible star has moves in a circle of radius r1 and has orbital period T. Variations in the brightness of nearby stars suggest that the unseen companion moves in a circle of radius r2 (see the figure). Find the approximate masses (a) m1 of the visible star and (b) m2 of the dark star. Express your answer in terms of r1, r2, T, and G. I asked this question before and recieved an incorrect answer, so I'm asking again.1. Consider a mass m initially at rest at a large distance I from center of the earth (l>R the earth's radius). The mass m is released and falls toward the earth. (a) Calculate the speed of the mass as a function of its distance x from the center of the earth. (b) In the approximation that l>>R, how much time does it take for the mass m to reach the earth? Express your answers in terms of R, 1, g (acceleration at the earth's surface) and (for part a) x.(a) Imagine that a space probe could be fired as a projectile from the Earth's surface with an initial speed of 5.96 x 10“ m/s relative to the Sun. What would its speed be when it is very far from the Earth (in m/s)? Ignore atmospheric friction, the effects of other planets, and the rotation of the Earth. (Consider the mass of the Sun in your calculations.) 354790 Your response differs from the correct answer by more than 100%. m/s (b) What If? The speed provided in part (a) is very difficult to achieve technologically. Often, Jupiter is used as a "gravitational slingshot" to increase the speed of a probe to the escape speed from the solar system, which is 1.85 x 10“ m/s from a point on Jupiter's orbit around the Sun (if Jupiter is not nearby). If the probe is launched from the Earth's surface at a speed of 4.10 × 10“ m/s relative to the Sun, what is the increase in speed needed from the gravitational slingshot at Jupiter for the space probe to escape the solar system (in m/s)? (Assume…
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- = 400 kg with their centers 8 meters apart. If you In the simulation, start with mị = 200 kg and m2 want to increase in the gravitational force between the two masses by the greatest amount, should you double the mass of m2 or should you halve the distance between the masses? In one or two sentences, explain which option would create the greater increase in the gravitational force and why.The Earth is about 81 times more massive than the Moon.The Earth and the Moon apply gravitational forces to each other. The magnitude of the gravitational force acting on the Earth is the gravitational force acting on the Moon.a greater thanb) equal toc) less thand) not enough information to tellThe planet, named 581 c that has a radius that is 1.5 times the radius of Earth. If the acceleration of the gravity on the surface of the planet 581 c, g 581c = 2.22 g Earth. Find the mass of the planet 581 c.