Concept explainers
Orbit of a Satellite A satellite is in orbit around the moon. A coordinate plane containing the orbit is set up with the center of the moon at the origin, as shown in the graph, with distances measured in megameters (Mm). The equation of the satellite’s orbit is
- (a) From the graph, determine the closest and the farthest that the satellite gets to the center of the moon.
- (b) There are two points in the orbit with y-coordinates 2. Find the x-coordinates of these points, and determine their distances to the center of the moon.
(a)
The closest and the farthest points that the satellite gets to the center of the moon in the graph.
Answer to Problem 115E
The closest and the farthest points that the satellite gets to the center of the moon in the graph is
Explanation of Solution
Given:
The equation of satellite’s orbit is,
And the graph of orbit with the centre of the moon at the origin is,
Figure (1)
Calculation:
The closest and farthest points in satellite’s orbit can be found by the intersection points of equation
Substitute 0 for y in orbit equation
Further solve,
So the closest and the farthest points that the satellite gets to the center of the moon in the graph is
(b)
The x-coordinates of points in the orbit with y-coordinates 2 and find their distances to the center of moon.
Answer to Problem 115E
The x-coordinates of points in the orbit with y-coordinates 2 is 7.3303 and
Explanation of Solution
Given:
The equation of satellite’s orbit is,
And the graph of orbit with the centre of the moon at the origin is,
Figure (1)
Calculation:
The x-coordinates of the points in the orbit with y-coordinates 2 is,
Further solve,
So the two value of x is
And the distance of the point
So distance of the point
And the distance of the point
So distance of the point
Chapter 1 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning