a ship is orbiting a planet (M = 3.0 x 10^24 kg with a radius R = 3,600 km) roughly 10,000 km from the planets surface. a) determine the force of gravity acting on the ship? b) what is the orbital velocity of a ship circling the planet at this distance? c) what is the period of rotation (T) of the ship in this orbit?

A geosynchronous Earth satellite is one that has an orbital period of precisely 1 day. Such orbits are useful for communication and weather observation because the satellite remains above the same point on Earth (provided it orbits in the equatorial plane in the same direction as Earth’s rotation). Calculate the radius of such an orbit based on the data for Earth in Appendix D.

1) How does the acceleration due to gravity at the surface of a planet change if the planet's radius is doubled ?

Two planets P, and P, orbit around a star S in circular orbits with speeds v, = 46.4 km/s, and v, = 57.4 km/s respectivel (a) If the period of the first planet P, is 710 years what is the mass, in kg, of the star it orbits around? kg (b) Determine the orbital period, in years, of P2. yr

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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…

Astronomers discover an exoplanet, a planet orbiting a star other than the Sun, that has an orbital period of 2.25 Earth years in a circular orbit around its star, which has a measured mass of 3.80×1030 kg. a) What is the radius of the orbit in meters? b) If the exoplanet has a mass of 6.100x10 24kg and a radius of 6520km, what will be the acceleration due to gravity on the surface of the exoplanet?

A 686-kg satellite is in a circular orbit about Earth at a height above Earth equal to Earth's mean radius. (a) Find the satellite's orbital speed. m/s (b) Find the period of its revolution. (c) Find the gravitational force acting on it. Need Help? Read It

The spaceship Palomino approaches star XYZ to study it by going into a circular orbit of radius 1.0·107 km. All that is known initially is that a planet orbits this star at a distance of 1.86·108 km taking a time of 271 Earth-days to make one full orbit. At what speed should the ship orbit the star at? What is the gravitational acceleration on the Palomino due to this star's gravity? (c) What is the ratio of the mass of star XYZ with that of the Sun? (MSun = 1.987·1030 kg)

11 Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.0 x 10- solar masses. A star orbiting near the galaxy's periphery is 5.9 x 10" light-years from its center. (a) What should the orbital period (in y) of that star be? y. (b) If its period is 6.1 x 10' years instead, what is the mass (in solar masses) of the galaxy? Such calculations are used to imply the existence of other matter, such as a very massive black hole at the center of the Milky Way. solar masses