How much work is required to lift a 500-kg satellite to an altitude of 3⋅10^6 m above the surface of the Earth? The gravitational force is F=GMm/r^2, where M is the mass of the Earth, m is the mass of the satellite, and r is the distance between the satellite and the Earth's center. The radius of the Earth is 6.4⋅10^6 m, its mass is 6⋅10^24 kg, and in these units the gravitational constant, G, is 6.67⋅10^−11. Work=  (include units)

A new planet named Vulcan has been discovered. Vulcan is a rather large planet with a radius twice that of Earth and a mass three times that of Earth. An astronaut has a mass of 60.0 kg and weighs about 132 lbs. on Earth. If the astronaut is on the planet Vulcan, what is her weight? The following numerical values may be helpful in this question. G = 6.67 ∙10-11 N∙m2/ kg2 Earth’s mass = 5.98 · 1024 kilograms g = 9.80 m/sec2 1 kilometer = 1000 meters

A satellite m = 500 kg orbits the earth at a distance d = 199 km, above the surface of the planet. The radius of the earth is re=6.38×106 m and the gravitational constant G =6.67×10-11 N m2/kg2 and the Earth's mass is me=5.98×1024 kg. What is the speed of the satellite in m/s?

Two spherical objects have a combined mass of 160 kg . The gravitational attraction between them is 7.61×10−6 NN when their centers are 21.0 cm apart. What is the mass of the heavier object?   What is the mass of the lighter object?

Everyone knows the earth is pulled toward the Sun by the gravitational force between the Sun (M = 2 x 10^30kg) and the earth (m = 6 x 10^24kg).  What is the gravitational acceleration of the Sun due to the earth's pull (1.5 x 10^11 km apart)?

Scientists want to place a 4 × 103 kg satellite in orbit around Mars. They plan to have the satellite orbit a distance equal to 2.4 times the radius of Mars above the surface of the planet. Here is some information that will help solve this problem: mmars = 6.4191 x 1023 kgrmars = 3.397 x 106 mG = 6.67428 x 10-11 N-m2/kg2 1.)What is the force of attraction between Mars and the satellite? 2.)What speed should the satellite have to be in a perfectly circular orbit? 3.)How much time does it take the satellite to complete one revolution?

What is the escape speed from a planet of mass M = 3.1 x 1023 kg and radius R = 2.6 x 106 m? Write the answer in terms of km/s.

Newton's law of universal gravitation is represented by Mm F = G- where F is the gravitational force, M and m are masses, and r is a length. Force has the SI units kg · m/s2. What are the SI units of the proportionality constant G? m3 kg - s2 m kg ·s3 m2 kg · s2 m2 kg · 3

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

Comets travel around the sun in elliptical orbits with large eccentricities. If a comet has speed 3.1x10^4 m/s when at a distance of 2.7x10^11 m from the center of the sun, what is its speed when at a distance of 4.7x10^10 m? Mass of the Sun is 1.99×10^30 kg. Gravitational constant is G=6.67×10^(−11) m^3 /(kg⋅s).   What is the formula?   (Answer: 75006.70209088 m/s)