By what factor will the acceleration due to gravity change if the mass of a planet is double and the size of the planet is also doubled?

Newtons version of Kepler's third law is P2=4pi2/(G(M1+M2)) x a3. Since the square of the period P varies inversely with the Sum of the masses (M1+M2), the period itself depends on the inverse square root of the object masses. If a solar system has a star that is 3.9 times as massive as our Sun, and if that solar system has Earths exact twin, what is the orbital period of that planets months ?

Two newly discovered planets follow circular orbits around a star in a distant part of the galaxy. The orbital speeds of the planets are determined to be 39.5 km/s and 58.5 km/s. The slower planet's orbital period is 6.68 years. (a) What is the mass of the star? (b) What is the orbital period of the faster planet, in years? (a) Number i (b) Number i Units Units ◄►

You are visiting a newly discovered exoplanet (mass M and radius R) that completes one rotation about its axis every 12 hours (Earth hours). You place your spaceship in a geostationary orbit at an altitude h = 6R above the planet's surface. While in orbit you decided to beam down to the planet to investigate the surface. While on the surface you perform a simple kinematics experiment and discover that the gravitational acceleration at the surface is ap = 0.60g, where g is the gravitational acceleration on the Earth's surface. You can assume that the exoplanet is a uniform sphere, and that your spaceship's orbit is circular. Note: A geostationary orbit is a special type of geosynchronous orbit where the satellite/spaceship remains at the same position above the equator throughout its orbit. Technically the prefix "geo" indicates the Earth, but we'll go ahead and use the term here in reference to this new planet. (a) What is the radius of the planet? R = km (b) What is the mass of the…

An object of mass m is released from rest a distance R above the surface of a planet of mass M and radius R.  Derive an expression for the speed with which it hits the planet’s surface v.

Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8 x 1011 solar masses. A star orbiting near the galaxy's periphery is 5.6 x 104 light years from its center. (For your calculations, assume that the galaxy's mass is concentrated near its center.) (a) What should the orbital period of that star be? yr (b) If its period is 5.1 x 107 years instead, what is the mass of the galaxy? Such calculations are used to imply the existence of "dark matter" in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies. solar masses