The state vectors for an Earth-orbiting spacecraft at a given point in time are: =(2,200 / +1,300 J+ 6,400 R) km and V = (3.21+5.2J +4.7 R) km/s What is the semi-major axis of the orbit? a. 6,203 km 7,078 km 9,122 km č. d. None of the above 9:-M २६ = -3.986 x 10 k.

The radius and mass of a planet are 5.39E+06_m and 2.56E+25_kg, respectively. A spaceship is in orbit at a distance of 1680_km above the surface of the planet. Find the orbital speed of the ship. 4. 12990_m/s 15540_m/s F. А. 13670 _m/s D. В. 14650_m/s E. C. 14180_m/s 12170_m/s

The position of a planet that a closest to and farthest from the sun are called its perihelion and aphelion respectively. We know that the Earth orbits around the Sun (as one focus) in an elliptical orbit with the perihelion distance of 1.47 x 10^8 km and the aphelion distance of 1.52 x 10^8 km. Find the Cartesian equation of the elliptical orbit.

Planet X with a radius of 4.0 Rearth⊕ is found orbiting a star of mass 0.80M⊙ . The eccentricity of its orbit is 0.05, and at its farthest approach to the star, it is 0.63 AU away, while at its closest approach to the star, it is 0.57 AU away.  a. How long does it take Planet X to make a complete orbit around its star in years? b.The semi major axis of the planet is changed such that its closest approach to the star is now 2.9 AU. Would the gravitational force exerted by the star on Planet X increase or decrease? By what factor? Would the gravitational force exerted by Planet X on the star increase or decrease? By what factor?  c. The mass of the star was increased to 2.4M⊙ . Would the gravitational force exerted by it on Planet X increase or decrease? By what factor? Would the gravitational force exerted by Planet X on the star increase or decrease? By what factor?   d. What must the mass of Planet X be in Mearth⊕ such that an astronaut on its surface would have the same weight as…