Problem 1: 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 finding the gravitational field g due to the Moon or the Sun, which is the acceleration that the Earth would have if it 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 10° kilometers away from the Earth. The Sun, meanwhile, has a mass of 1.99 x 1030 kilograms and is located 1.49 x 10 kilometers away from the Earth. Part (a) Calculate the magnitude of the gravitational field of the moon at the location of Earth, in meters per square second. Numeric : A numeric value is expected and not an expression. §M = Part (b) Calculate the magnitude of the gravitational field of the Sun at the location of Earth, in meters per square second. Numeric : A numeric value is expected and not an expression. gs = Part (c) Calculate the ratio of the gravitational field of the Sun to the gravitational field of the Moon, at the location of Earth. Numeric : A numeric value is expected and not an expression. gs/gM =

Problem 1: 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 finding the gravitational field g due to the Moon or the Sun, which is the acceleration that the Earth would have if it 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 10° kilometers away from the Earth. The Sun, meanwhile, has a mass of 1.99 x 1030 kilograms and is located 1.49 x 10 kilometers away from the Earth. Part (a) Calculate the magnitude of the gravitational field of the moon at the location of Earth, in meters per square second. Numeric : A numeric value is expected and not an expression. §M = Part (b) Calculate the magnitude of the gravitational field of the Sun at the location of Earth, in meters per square second. Numeric : A numeric value is expected and not an expression. gs = Part (c) Calculate the ratio of the gravitational field of the Sun to the gravitational field of the Moon, at the location of Earth. Numeric : A numeric value is expected and not an expression. gs/gM =

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter6: Energy Of A System

Section: Chapter Questions

Problem 15OQ

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(a) Find the magnitude of the gravitational force between a planet with mass 7.50 1024 kg and its moon, with mass 2.70 1022 kg, if the average distance between their centers is 2.80 108 m. (b) What is the acceleration of the moon towards the planet? (c) What is the acceleration of the planet towards the moon?
The gravitational force exerted on an astronaut on the Earths surface is 650 N directed downward. When she is in the space station in orbit around the Earth, is the gravitational force on her (a) larger, (b) exactly the same, (c) smaller, (d) nearly but not exactly zero, or (e) exactly zero?
Let gM represent the difference in the gravitational fields produced by the Moon at the points on the Earths surface nearest to and farthest from the Moon. Find the fraction gM/g, where g is the Earths gravitational field. (This difference is responsible for the occurrence of the lunar tides on the Earth.)
The Sun has a mass of approximately 1.99 1030 kg. a. Given that the Earth is on average about 1.50 1011 m from the Sun, what is the magnitude of the Suns gravitational field at this distance? b. Sketch the magnitude of the gravitational field due to the Sun as a function of distance from the Sun. Indicate the Earths position on your graph. Assume the radius of the Sun is 7.00 108 m and begin the graph there. c. Given that the mass of the Earth is 5.97 1024 kg, what is the magnitude of the gravitational force on the Earth due to the Sun?
Calculate the effective gravitational field vector g at Earths surface at the poles and the equator. Take account of the difference in the equatorial (6378 km) and polar (6357 km) radius as well as the centrifugal force. How well does the result agree with the difference calculated with the result g = 9.780356[1 + 0.0052885 sin 2 0.0000059 sin2(2)]m/s2 where is the latitude?
Suppose the gravitational acceleration at the surface of a certain moon A of Jupiter is 2 m/s2. Moon B has twice the mass and twice the radius of moon A. What is the gravitational acceleration at its surface? Neglect the gravitational acceleration due to Jupiter, (a) 8 m/s2 (b) 4 m/s2 (c) 2 m/s2 (d) 1 m/s2 (e) 0.5 m/s2
(a) Find the magnitude of the gravity force between a planet with mass 5.98 1024 kg and its moon, with mass 7.36 1022 kg, if the average distance between them is 3.84 108 m. (b) What is the acceleration of the moon toward the planet? (c) What is the acceleration of the planet toward the moon? (See Section 7.5.)
How far from the center of the Sun would the net gravitational force of Earth and the Sun on a spaceship be zero?
What is the orbital radius of an Earth satellite having a period of 1.00 h? (b) What is unreasonable about this result?
For many years, astronomer Percival Lowell searched for a Planet X that might explain some of the perturbations observed in the orbit of Uranus. These perturbations were later explained when the masses of the outer planets and planetoids, particularly Neptune, became better measured (Voyager 2). At the time, however, Lowell had proposed the existence of a Planet X that orbited the Sun with a mean distance of 43 AU. With what period would this Planet X orbit the Sun?
In the law of universal gravitation, Newton assumed that the force was proportional to the product of the two masses (m1m2) . While all scientific conjectures must be experimentally verified, can you provided arguments as to why this must be? (You may wish to consider simple examples in which any other form would lead to contradictory results.)
A space probe is launched from Earth headed for deep space. At a distance of 10,000 km from Earth's center, the gravitational force on it is 900 N. What is the magnitude of the force when the probe is 30,000 km from Earth's center?