Given that the distance between the center of the earth and the moon is D, if the mass of the earth is Mearth and the mass of the moon is Mmoon, what is the expression for the acceleration of an object half way between the earth and the moon (in other words it has a distance 1/2 D from the center

On a planet whose radius is 1.5 x 10^7 m, the acceleration due to gravity is 20 meter per second square. An astronaut with a mass of 66 kg is standing on this planet. Find the mass of the planet?

Astronomers have observed a small, massive object at the center of our Milky Way Galaxy. A ring of material orbits this massive object; the ring has a diameter of about 17 light-years and an orbital speed of about 100 km/s. A) Determine the mass  M  of the massive object at the center of the Milky Way Galaxy. Give your answer in kilograms.Express your answer in kilograms. B) Give your answer in solar masses (one solar mass is the mass of the sun). Express your answer in units of solar masses. C) Many astronomers believe that the massive object at the center of the Milky Way Galaxy is a black hole. If so, what must the Schwarzschild radius  RS of this black hole be? Express your answer in meters.

In the book 2010: Odyssey Two, Chinese astronauts land on Europa, one of Jupiters Moons. Suppose one of these astronauts on Europa drops a tool 2 m above the ground. How long will it take for it to hit the ground?  MEuropa = 4.7998×1022 kg, REuropa = 1.561×106

(a) Find the magnitude of the gravitational force (in N) between a planet with mass 7.75 x 1024 kg and its moon, with mass 2.50 × 1022 kg, if the average distance between their centers is 2.70 x 108 m. N (b) What is the moon's acceleration (in m/s²) toward the planet? (Enter the magnitude.) m/s² (c) What is the planet's acceleration (in m/s²) toward the moon? (Enter the magnitude.) m/s²

On a planet whose radius is 1.80 × 104 km, the acceleration due to gravity is 16.5 m/s?. What is the mass of the planet?

Concern the planet Mars, which has a radius of 3400 km. On Mars, the acceleration due to gravity is 3.72 m/s^2 The mass of the sun is 2.0×1030 kg, while the (actual) mass of Mars is 6.4×1023 kg. The average distance from Mars to the sun is 228 million kilometers. a. What is the gravitational force acting on Mars due to the sun? What is the reaction force to this force? Name or explain the force; don’t give a value. b. What are the speed and angular velocity of Mars? Compare the values to those of Earth. c. Using only information provided above, estimate the length of a year on Mars. Compare the value to that of Earth.

Two masses (m1 = 5x105 kg and m2 = 5 x105 kg ) are separated by 1 m. What is the magnitude of the force of gravity acting on each mass (in Newtons)?

(a) Find the magnitude of the gravitational force (in N) between a planet with mass 8.00 x 1024 kg and its moon, with mass 2.20 x 1022 kg, if the average distance between their centers is 2.90 × 108 m. N (b) What is the moon's acceleration (in m/s2) toward the planet? (Enter the magnitude.) m/s² (c) What is the planet's acceleration (in m/s2) toward the moon? (Enter the magnitude.) m/s²

An astronaut standing on Earth’s surface has a weight of 700 N (about 157 lbs). He then takes a rocket ship to a distant planet with a mass twice as large as Earth and a radius 50% larger than Earth’s radius. How much does the astronaut weigh on this new planet (in Newtons)?