An exoplanetary system has two known planets. Planet X orbits in 290 days and Planet Y orbits in 145 days.  Which planet is closest to its host star?   If the star has the same mass as the Sun, what is the semi-major axis of the orbits for Planets X and Y?

Satellite 1 has a mass m_1m1​ and is located a distance r_1r1​ away from the center of its host planet. Satellite 2 has half the mass as Satellite 1, but is located four-times the distance from the center of the host planet as Satellite 1. Determine the ratio of the magnitudes of the force of gravity between Satellite 1 and the planet to the force of gravity between Satellite 2 and the planet Ratio = Fplanet-on-1/ Fplanet-on-2

Exoplanets A and B are observed to orbit Star X in circular orbits at distances 1.1 AU and 10.2 AU from Star X, respectively ( 1 AU = 1.5 x 1011 m) . The orbital period of Exoplanet A is 244 days. What is the mass of Star X? (1 day = 86400 s.)

You have negotiated with the Omicronians for a base on the planet Omicron Persei 7. The architects working with you to plan the base need to know the acceleration of a freely falling object at the surface of the planet in order to adequately design the structures. The Omicronians have told you that the value is  gOP7=7.29 flurg/grom^2, but your architects use the units meters/second^2, and from your previous experience you know that both the Omicronians and your architects are terrible at unit conversion. Thus, it's up to you to do the unit conversion. Fortunately, you know the unit equality relationships: 5.24flurg=1meter and 1grom=0.493second. What is the value of  gOP7 in the units your architects will use, in meter per second squared?

The supermassive black hole at the center or our galaxy (Sagittarius A*) has a mass equal to 4.3 million Suns (the mass of the Sun is 1.99 × 1030 kg). The distance from Sgr A* to Earth is 7,940 parsecs, where one parsec is equal to 3.09 × 1016 m. (a) What is the gravitational force that Sgr A* exerts on a 75 kg person on Earth, in units of Newtons? Hint: use Newton's law of universal gravitation. (b) Suppose the same person is sitting 1.0 meter away from a paperclip with a mass of 1.0 grams. What is the gravitational force that the paperclip exerts on the person? (c) Compare the forces from parts (a) and (b). Which is greater?

What is the escape velocity is km/s from Jupiters exosphere, which begins about 993 km above the surface ? Assume the Gravitational constant is G= 6.67 x10-11m3 kg-1s-2, and that's Jupiter has a mass of 1.8999999999999998e+27kg and a radius of 68.0 x103km

Neptune has a mass of 1.0 × 1026 kg and is 4.5 × 109 km from the Sun with an orbital period of 165 years. Planetesimals in the outer primordial solar system 4.5 billion years ago coalesced into Neptune over hundreds of millions of years. If the primordial disk that evolved into our present day solar system had a radius of 1011 km and if the matter that made up these planetesimals that later became Neptune was spread out evenly on the edges of it, what was the orbital period of the outer edges of the primordial disk?