A spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system ? Mass of the space ship = 1000 kg; mass of the sun = 2×1030 kg; mass of mars = 6.4×1023 kg; radius of mars = 3395 km; radius of the orbit of mars = 2.28 ×108 km; G = 6.67×10-11 N m2 kg-2

The International Space Station, which has a mass of 4.94×105 kg, orbits 258 miles above the Earth's surface, and completes one orbit every 94.3 minutes. What is the kinetic energy of the International Space Station in units of GJ (109 Joules)? (Note: don't forget to take into account the radius of the Earth!) Enter answer here GJ

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)

The first asteroid to be discovered is Ceres. It is the largest and most massive asteroid is our solar system’s asteroid belt, having an estimated mass of 2.0 x 1021 kg and an orbital speed of 18100 m/s. Determine the amount of kinetic energy possessed by Ceres.

Jupiter's moon Io has active volcanoes (in fact, it is the most volcanically active body in the solar system) that eject material as high as 500 km (or even higher) above the surface. Io has a mass of 8.93×1022kg8.93×1022kg and a radius of 1821 km. How high would this material go on earth if it were ejected with the same speed as on Io? (RE = 6370 km, mE=5.96×1024kg)

Part A Comets travel around the sun in elliptical orbits with large eccentricities. If a comet has speed 2.1×104 m/s when at a distance of 2.6x1011 m from the center of the sun, what is its speed when at a distance of 4.0×1010 m. Express your answer in meters per second. Πνα ΑΣΦ m/s

CM-2 A water molecule consists of an oxygen atom with y a mass of 16.0u (u is one atomic mass unit) and two hydrogen atoms, each with a mass of 1.00u. The distance of each hydrogen atom from the center of the oxygen atom is 0.100nm (n=10"). The angle between the hydrogen atoms is 106°. Suppose that a coordinate system is used such that the x axis splits the angle between the two hydrogen atoms as shown to the right. a) Find the y coordinate of the center of mass of the water molecule. b) Find the x coordinate in nm of the center of mass of the water molecule. 0.100nm, 53.0° 53.0° 0.100nm 梦 0 hp

Venus is known as the 'Earth's sister' because of its similar size and gravity. It has a mass of 4.87 x 10^24 kg and an average radius of 6060 km. As the 150 kg satellite slowly approaches the surface of Venus it is influenced by its gravitational field. (a) Describe how the satellite gravitational potential energy changes as it is moving from an altitude of 5000 km to the surface of Venus.   (b) Calculate the gravitational fieid strength on the surface of Venus.

1. What is the gravitational potential energy in a system of three objects with masses m₁ = 2.0 × 1020 kg, m2 = 4.0 × 1020 kg, and m3 1.0 × 1021 located at r₁ = 2.0 × 10¹3 m 1.0 × 106 m -1.3 × 10¹2 m 1 respectively? 9 r2 = -6.0 × 10¹3 m 2.2 × 10¹² m –5.7 × 10³ m {] 9 T3 = = 1.5 × 10¹1 m −6.5 × 10² m 9.2 × 10¹0 m

At its closest distance from Earth, the moon experiences a gravitational force of 2.22 E 20 N. The mass of the Earth is 5.97 E24 kg. The mass of the moon is 7.35 E22 kg. What is the distance between the Earth and the moon at that point if G = 6.67 E−11 N*m2/kg2?  1. 1.32 E 4 km  2. 3.63 E 6 km  3. 3.63 E 8 km  4. 1.32 E 17 km