(a)
To calculate: Formula for the mass of a planet according to Kepler granted that the mass of a planet with a satellite is directly proportional to the cube of the mean distance from the satellite to the planet, and inversely proportional to the square of the period of revolution.
(b)
To calculate: The proportionality constant using the observations and estimates for the earth and the moon granted that the mass of the earth,
(c)
To calculate: The mass of the Mars granted that the period of revolution,
(d)
To calculate: The approximate ratio of the mass of the earth to the mass of Mars granted that the Mass of the earth,
(e)
To calculate: The mean distance between Io and the Jupiter granted that the mass of the Jupiter,
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
College Algebra (6th Edition)
- The Kelvin Temperature Scale Physicists and chemists often use the Kelvin temperature scale. In order to determine the relationship between the Fahrenheit and Kelvin temperature scales, a lab assistant put Fahrenheit and Kelvin thermometers side by side and took readings at various temperatures. The following data were recorded. K = kelvins F = degrees Fahrenheit 200 -99.67 220 -63.67 240 -27.67 260 8.33 280 44.33 300 80.33 a. Show that the temperature F in degrees Fahrenheit is a linear function of the temperature K in kelvins. b. What is the slope of this linear function? Note: Be sure to take into account that the table lists kelvins in jumps of 20 rather than in jumps of 1. c. Find a formula for the linear function. d. Normal body temperature is 98.6 degrees Fahrenheit. What is that temperature in kelvins? e. If temperature increases by 1 kelvin, by how many degrees Fahrenheit does it increase? If temperature increases by 1 degree Fahrenheit, by how many kelvins does it increase? f. The temperature of 0 kelvins is known as absolute zero. It is not quite accurate to say that all molecular motion ceases at absolute zero, but at that temperature the system has its minimum possible total energy. It is thought that absolute zero cannot be attained experimentally, although temperatures lower than 0.0000001 kelvin have been attained. Find the temperature of absolute zero in degrees Fahrenheit.arrow_forwardFrictional Force The frictional force F between the tires and the road required to keep a car on a curved section of a highway is directly proportional to the square of the speed s of the car. If the speed of the car is doubled, the force will change by what factor?arrow_forwardMosteller Formula for Body Surface Area: Body surface area is an important piece of medical information because it is a factor in temperature regulation as well as some drug level determinations. The Mosteller formula gives one way of estimating body surface area B in square meters. The formula uses the weight w in kilograms and the height h in centimeters. The relation is B=hw60 In this exercise, we consider people who are 190 centimeters tall. a. Write a formula for B as a function of w. b. Make a graph of B versus w. includes weights up to 100 kilograms. c. Is the graph you made in part b concave up or concave down? d. In this part, we consider the effect of weight gain on men who are 190 centimeters tall. Would the weight gain have a greater effect on surface area for a lighter man or for a heavier man?arrow_forward
- Ohms Law: says that when electric current is flowing across a resistor, the current i, measured in amperes, can be calculated from the voltage v, measured in volts, and the resistance R, measured in ohms. The relationship is given by i=vRamperes. a. A resistor in a radio circuit is rated at 4000 ohms. i. Find a formula for the current as a function of the voltage. ii. Plot the graph of i versus v. include values of the voltage up to 12 volts. iii. What happens to the current when the voltage increases? b. The lights on your car operate on a 12-volt battery. i. Find a formula for the current in your car lights as a function of the resistance. ii. Plot the graph of i versus R. We suggest a horizontal span here of 1 to 25. iii. What happens to the current when the resistance increases?arrow_forwardSpeed of a Skidding Car Police use the formula s=30fd To estimate the speed s (in mi/h) at which a car is traveling if it skids d feet after the brakes are applied suddenly. The number f is the coefficient of friction of the road, which is a measured of the “slipperiness” of the road. The table gives some typical estimates for f . If a car skids 65 ft. on wet concrete, how fast was is moving when the brakes were applied? If a car is traveling at 50 mi/h, how far will it skid on wet tar?arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage