Pls provide step by step workings for each question

A2 1. 2. A 65.0 kg astronaut is walking on the surface of the Moon, which has a mean radius of 1.74 x 103 km and a mass of 7.35 x 1022 kg. What is the weight of the astronaut? In an experiment, an 8.0 kg lead sphere is brought close to a 1.5 kg mass. The gravitational force between the two objects is 1.28 x 10'8 N. How far apart are the centres of the objects? The radius of the planet Uranus is 4.3 times the radius of Earth. The mass of Uranus is 14.7 times the mass of Earth. How does the gravitational force on the surface of Uranus compared to that on Earth? Eris, a dwarf planet, is the ninth most massive body orbiting the Sun. It is more massive than Pluto and three times farther away from the Sun. Eris is estimated to have a radius of approximately 1200 km. a. Suppose that an astronaut stands on Eris and drops a rock from a height of 0.30 m. The rock takes 0.87 s to reach the surface. Calculate the value of g on Eris. b. Calculate the mass of Eris. Three large, spherical asteroids in space are arranged at the corners of a right triangle as shown. Given the following information find the net force on asteroid A due to asteroid B and C. .V In mA = 1.0 x1020 kg --x mB = 2.0 x1020 kg rAB = 5.0 x 1010 m mC = 4.0 x 1020 kg rAC = 2.5 x 1010 m A3 Calculate the magnitude of the gravitational field strength on the surface of Saturn, assuming that it is perfectly spherical with a radius of 6.03 x 107 m. The mass of Saturn is 5.69 x1026 kg. On the surface of Titan, a moon of Saturn, the gravitational field strength has a magnitude of 1.3 kag. Titan's mass is 1.3 x 1023 kg. What is Titan's radius? Suppose that an object expanded until its radius doubled, while its mass stayed the same. Determine the effect on its gravitational eld strength. Suppose that the mass of a planet doubled but its radius stayed the same. Determine the effect on its gravitational field strength. A4 1. Determine the speeds of Venus and Earth as they orbit the Sun. Venus has an orbital radius of 1.08 x 1011 m while Earth has an orbital radius of 1.49 x 1011 m. The mass of the Sun is 1.99 x1030 kg. 2. Material has been observed in a circular orbit around a black hole some five thousand light-years away from Earth. Spectroscopic analysis of the material indicates that it is orbiting with a speed of 3.1 x 107 mfs. If the radius of the orbit is 9.8 x 105 m, determine the mass of the black hole, assuming the matter being observed moves in a circular orbit around it. 3. What is the difference between a geosynchronous orbit and a geostationary orbit? 4. The International Space Station orbits Earth at an altitude of ~ 350 km above Earth's surface. lfthe mass of the Earth is ~ 5.98 x 1024 kg and the radius of Earth is ~ 6.38 x 106 m, determine the speed needed by the ISS to maintain its orbit. (Hint: rISS = rem + I,altitude) A5 1. Suppose you have two boxes of electrons, each with a total charge of qT = -1.8 x 108 C separated by a distance of 1.0 m. Determine the magnitude of the electric force between the two boxes. (For simplicity, assume that each box is so small that it can be modelled as a point charge.) A small sphere, carrying a charge of -8.0 uC, exerts an attractive force of 0.50 N on another sphere carrying a charge of magnitude 5.0 uC. (Note: u = 10'3 ) a. What is the sign of the second charge? b. What is the distance of separation of the centres of the spheres? Two charged spheres, 5.0 cm apart, attract each other with a force of 24 N. Determine the magnitude of the charge on each, if one sphere has four times the charge (of the opposite sign) as the other. Two oppositely charged objects exert a force of attraction of 8.0 N on each other. What will be the new force of attraction if: a. the charge on one object is halved? b. the charge on one object is tripled? c. the charge on each object is doubled? d. the distance between the charges is doubled