In a certain binary-star system, each star has the same mass which is 9.0 times of that of the Sun, and they revolve about their center of mass. The distance between them is the 7.9 times the distance between Earth and the Sun. What is their period of revolution in years?

The 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.)

(a) A planet is in an elliptical orbit around a distant star. At its closest approach, the planet is 0.580 AU from the star and has a speed of 54.0 km/s. When the planet is at its farthest distance from the star of 37.0 AU, what is its speed (in km/s)? (1 AU is the average distance from the Earth to the Sun and is equal to 1.496 x 10¹¹ m. You may assume that other planets and smaller objects in the star system exert negligible forces on the planet.) km/s (b) What If? A comet is in a highly elliptical orbit around the same star. The comet's greatest distance from the star is 20,900 times larger than its closest distance to the star. The comet's speed at its greatest distance is 2.70 x 10-² km/s. What is the speed (in km/s) of the comet at its closest approach? km/s