Problem 3: In this problem we are going to compare the strength of the gravitational interaction between the Moon and the Earth and the Sun and the Earth. We will do this by nding the gravitationaleld g due to the Moon or the Sun, which is the acceleration that the Earth would have ifit were interacting with each of them. For reference, the Moon has a mass of 7.34 X 1022 kilograms and is located 3.84 X 105 kilometers away from the Earth. The Sun, meanwhile, has a mass of 1.99 X 1030 kilograms and is located 1.49 X 108 kilometers away from the Earth. Part (3} Calculate the magnitude of the gravitational eld of the moon at the location of Earth, in meters per square second. Numeric : A numeric value is expected and not an expression. 3M: Part (h) Calculate the magnitude of the gravitational eld of the Sun at the location of Earth, in meters per square second. Numeric : A numeric value is expected and not an expression. RS: Part (c) Calculate the ratio of the gravitational eld of the Sun to the gravitational eld of the Moon, at the location of Earth. Numeric : A numeric value is expected and not an expression. A's/RM = Problem 4: An intergalactic spaceship arrives at a distant planet that rotates on its axis with a period of T. The spaceship enters a geosynchronous orbit at a distance of R. ' lltu'xl'ur'lt.1.rmn Part (a) From the given information, write a general expression for the mass of the planet in terms of G and the variables from the problem statement. Expression M: Select from the variables below to write your expression. Note that all variables may not be required. a, 3.1L 9, d, G, h,j, k, m, n, P, q, R, T Part (b) Calculate the mass ofthe planet in kilograms if T: 57hours and R : 2.2 x 108 m. Numeric : A numeric value is expected and not an expression. M: Problem 5: A meteoroid is moving towards a planet. It has mass m = 0.46x109 kg and speed v1 = 3.8x10' m/s at distance R1 = 2. 7x10' m from the center of the planet. The radius of the planet is R = 0.38x10' m. The mass of the planet is M = 8.4x1025 kg. There is no air around the planet. .R1 .. theexpertta.com Part (a) Enter an expression for the gravitational potential energy PE, of the meteoroid at R1 in terms of defined quantities and the gravitational constant G. Assume the potential energy is zero at infinity. Expression : PE1 Select from the variables below to write your expression. Note that all variables may not be required. a, B, 0, d, g, G, h, m, M, P, R, R1, t, v, v1 Part (b) Calculate the value of PE1, in joules. Numeric : A numeric value is expected and not an expression. PE1 Part (c) Enter an expression for the total energy E1 of the meteoroid at R1 in terms of defined quantities. Expression Select from the variables below to write your expression. Note that all variables may not be required. a, p, 0, d, g, G, h, m, M, P, R, R1, t, v, V1 Part (d) Calculate the value of E1, in joules. Numeric : A numeric value is expected and not an expression. E1 Part (e) Enter an expression for the total energy E of the meteoroid at R, the surface of the planet, in terms of defined quantities and v, the meteoroid's speed when it reaches the planet's surface. Expression : E = Select from the variables below to write your expression. Note that all variables may not be required. a, B, 0, d, g, G, h, m, M, P, R, R1, t, v, V1 Part (f) Enter an expression for v, the meteoroid's speed at the planet's surface, in terms of G, M, v1, R1, and R. Expression : V = Select from the variables below to write your expression. Note that all variables may not be required. a, p, 0, d, g, G, h, m, M, P, R, R1, t, v, V1 Part (g) Calculate the value of v in meters per second. Numeric : A numeric value is expected and not an expression