Circular and Satellite Motion Legacy Problem #19 Guided Solution
Problem*
Determine the acceleration of the moon about the Earth. (GIVEN: MEarth = 5.98 x 1024 kg and Earth-moon distance = 3.84 x 108 m)
Audio Guided Solution
An object such as the moon is orbiting the earth in what is nearly a circular motion. The centripetal or inward force that acts upon the moon in order to allow the circular motion is the force of gravitational attraction between the moon and the earth. This F-grab value can be used to calculate the acceleration. We would have to take the F-grab and we'd have to divide it by the mass of the moon. When you do, you get an equation for the acceleration of the moon that goes something like A equal g times the mass of the earth divided by the separation distance squared. Now if I plug the mass of the earth into that equation and then divide by the square of this 3.84 times 10 to the 8th meters, I'll get the acceleration of the moon and its value is 2.706 times 10 to the negative third meters per second per second. I can round that to three significant digits, it becomes .00271 or 2.71 times 10 to the negative third meters per second per second.
Solution
2.71 x 10-3 m/s/s
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities in an organized manner. Equate given values to the symbols used to represent the corresponding quantity - e.g., \(\descriptive{m}{m,mass} = 61.7\unit{kg}\), \(\descriptive{v}{v,velocity} = 18.5 \unit{\meter\per\second}\), \(\descriptive{R}{R,radius} = 30.9\unit{m}\), \(F_\text{norm} = \colorbox{gray}{Unknown}\).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
Read About It!
Get more information on the topic of Circular and Satellite Motion at The Physics Classroom Tutorial.