Pls show step by step workings for each question. Thank you! Everything is included in order to complete the questions

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 N/kg. 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. Refer to Appendix C for required data. 1. What keeps the International Space Station and other satellites in their orbits around Earth? 3. lfwe represent the magnitude of Earth's surface gravitational field strength as 19, what are the magnitudes of the gravitational field strengths [in terms of g] at the following distances above Earth's surface: (a) 1.0 Earth radii, (b) 3.0 Earth radii. and (c) 4.2 Earth radii? 5. The Moon has a surface gravitational field strength of magnitude 1.6 N/kg. (a) What is the mass of the Moon? (Hint:The Moon's radius is in the appendix.) (b) What would be the magnitude of yourweight if you were on the Moon? A4 1. Determine the speeds of Venus and Earth as they orbit the Sun. Venus has an orbital radius of 1.08 x1011 m while Earth has an orbital radius of 1.49 x1011 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. If the 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 = rEarth + raltitude) 5. 1. Apply one of Kepler's laws to explain why we are able to observe comets close to Earth for only small time intervals compared to their orbital periods. (Hint: A comet's elliptical orbit is very elongated.) "1| '1 5" closest to the Sun ahou lar'Iar; l- - 'd '1"*' 'st "m ab '1. 'ly. 'l._ Ke'e. st. 0.. . \"ic. n. as dz \"st *n =1 . t rapidl, mu .ea... l'apib._,. 3. A nonrotating frame of reference placed at the centre of the Sun is very nearly an inertial frame of reference. Why is it not exactly an inertial frame of reference? 'i a ' 'oiJf. 1"Mar r'di' 'nrl'taro c '.- .1qu: . .. . |. . - 5. If a small planet were discovered with an orbital period twice that of Earth, how many times farther from the Sun is this planet located? t 'v 't ""te is"*nca. 4. th " -.~ *' ' *' ' ' - 7 L . ._ .IL . 7. Mars has two moons, Phobos and Deimos (Greek for"Fear" and \"Panic." companions of Mars. the god of war). Deimos has a period of 30 h 18 min and an average distance from the centre of Mars of 2.3 X 10\" km. The period of Phobos is 7 h 39 min. What is the average distance of Phobos from the centre of Mars? A5 1. 5. 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 [10. (Note: u = 10'6 ) 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? 3. Calculate the force between charges of 5.0 X 108 C and 1.0 X 1070 if they are 5.0 cm apart. a. Calculate the magnitude of the force a 1.5 x 105 C charge exerts an a 3.2 X 10'\" C charge located 1.5 m away. . TV ' rositel' harged spl' res. lvith \"entre o-ce '9 St arati 1m\"! ' ' t '. a'io t. \"it. fo. of 1gn 1( ." '7'9.\"|e.'n2,~ 1:. the ., 1L6 1.1. 'it a 1| Jtoti.carg. nt'c en. Del. 11]. 3thL ' 39\".... a. .16.. art, .1 eat 6. Two equal uniform spherical charges, each of magnitude 1.1 X 107 C, experi ence an electrostatic force of magnitude 4.2 X 10'4 N. How far apart are the centres of the two charges? A6 1. Three charges (q1 = -2.00 p0, q2 = -1.80 p0 and q3 = +1.50 uC) are located as shown. Calculate the net force on q3 due to q1 and q2. 31 9:? Ga _ = +:' _ 41.5mrl +4.an-.-| 2. Using the same charges, calculate the net force on (12 due to C11 and q3. 3. Three charges are arranged at the corners of right triangle as shown. What is the net force on charge C? A [+5.0yt'1l 511cm 1. A positive test charge, qT = +2.0 x 10'9 C, is placed in an electric eld and experiences a force of4.0 x 'l0'9 N[W]. a. What is the electric eld intensity at the location of the test charge? b. Predict the force that would result if the test charge were replaced by a charge of qT = +9.0 x10'6 C. 2. Two point charges (q1 = +3.3 x 10'9 C and q2 = 'l .0 x 10.3 C) are located 45 cm apart. a. A positive test charge is located between q1 and q2 and 27 cm from q1 along a line connecting q1 and q2. What is the net electric field intensity on the positive test charge? b. A new charge of +2.0 x 10'12 C is placed at P. Determine the electric force on this new charge. 3. In the diagram, A and C are situated as shown. What is the magnitude and direction of the electric field intensity at point B? 4. 1. A negative charge of 2.4 x 10'6 C experiences an electric force of magnitude 3.2 N. acting to the left. (a) Calculate the magnitude and direction of the electric field at that point. (b) Calculate the value of the field at that point ifa charge of 4.8 X 105 C replaces the charge of 2.4 X 10'5 C. 2. At a certain point Pin an electric field. the magnitude of the electric field is 12 N/C. Calculate the magnitude of the electric force that would be exerted on a point charge of 2.5 X 107 C, located at P. 3. Calculate the magnitude and direction of the electric field at a point 3.0 m to the right of a positive point charge of5.4 X 10'\" C