The Moon has a mass 7.35 × 1022 kg of and a radius of 1740 km. Air resistance can be neglected on the Moon. G = 6.67 × 10-11 m³ kg-1 s-2 is the universal gravitational constant. (a) If a ball is launched upwards from the surface of the moon with an initial speed of 1.15 km/s, what height maximum height above the surface of the moon will it reach? Give your answer in kilometers. (b) What is the escape speed of the moon? Give your answer in km/s.

A number of gas giant planets orbiting other stars at distances less than 1 A.U. have been discovered. Because of their proximity to their parent stars, and their compositional similarity to Jupiter, they have been labeled “Hot Jupiters”.   The orbital radius of one of these planets is 0.06 A.U. with average orbital speed 600 km/sec. What is the length of this planet’s year in Earth (solar) days?  Estimate the mass, M, of its parent star in terms of the mass of the sun (M) using Newton’s first form of Kepler’s 3rd Law. Calculate the star’s luminosity, L, in terms of the luminosity of the sun (L☉), Note: (LL=MM4where L ~ 4 × 1026 W ).  The radius of this planet is 1.5 times the radius of Jupiter. Assuming its equilibrium temperature is the temperature at which the planet radiates as much energy as it receives from its star, estimate the temperature of the planet. The value of the planet’s albedo is 0.8. (NOTE: The intensity of the star’s radiant power at a distance d from the star is…

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 8.93×1022kg 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? (REarth = 6370 km, mEartg=5.96×1024kg) NOTE: Your answer suggests that you have assumed constant gravitational acceleration over the whole height of the ejected debris. Note that the gravitational field changes quite significantly over this height.

Determine the gravitational force of attraction between the Earth and Jupiter given the mass of the earth is 6 x 10^24 kg, the mass of Jupiter is 1.9 x 10^27 kg and when closest, the average distance is about 5.88 x 10^11 m. Use scientific notation for final result. Use G= 6.7 x 10^-11 N-m^2/kg^2.

At what altitude above Earth's surface would the gravitational acceleration be 4.40 m/s²? (Take the Earth's radius as 6370 km.) Number Units

A ball traveling in a circle with a constant speed of 3.6 m/s has a centripetal acceleration of 7.0 m/s2. What is the radius of the circle? (Answer in meters.)

Newton's theory of gravity, together with the Cavendish experiment to measure the value of Newton's constant G, determines the acceleration due to gravity at the surface of a sphere. For example, the acceleration due to gravity at the surface of Earth is g 9.81 m/s^2. Calculate the acceleration due to gravity at the surface of the sun, which has mass 1.989x10 30 kg and 6.96x108 m. radius = (in m/s^2) A: 112.2 OB: 140.2 OC: 175.3 OD: 219.1 OE: 273.9 OF: 342.3 OG: 427.9 OH: 534.9

Planet Z-1 has a mass equal to one-third that of the Earth and a radius equal to one- third that of the Earth. With g representing the acceleration of gravity on the surface of Earth, the acceleration due to gravity on the surface of Z-1 is g/3 3g 6g g/9 8g

An object of mass m is dropped from height h above a planet of mass M and radius R. Find an expression for the object's speed as it hits the ground. Express your answer in terms of the variables m, M, h, R, and gravitational constant G.

(A) Find the magnitude of the gravitational force (in N) between a planet with mass 7.75 ✕ 1024 kg and its moon, with mass 2.35 ✕ 1022 kg, if the average distance between their centers is 2.20 ✕ 108 m.     (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