Circular and Satellite Motion Legacy Problem #20 Guided Solution
Problem*
Determine the acceleration of the Earth about the sun. (GIVEN: Msun = 1.99 x 1030 kg and Earth-sun distance = 1.50 x 1011 m)
Audio Guided Solution
An object such as the earth orbits the sun in what is nearly a circular type motion. The centripetal or inward force that is required for the circular motion is supplied by the force of gravitational attraction between the earth and the sun. If we wish to calculate the acceleration we need to take this net force or gravitational force and divide it by the mass of the earth. That would mean that we would have to take the G mass sun mass earth per r squared and divide it by the mass of the earth. When we do we get a new equation for the acceleration of the earth about the sun. Its value is big G times the mass of the sun divided by the separation distance squared. Where the big G is 6.673 times 10 to the negative 11th which is meters squared per kilogram squared and the mass of the sun is given here as 1.99 times 10 to the 30th kilogram. We have to substitute into the denominator 1.50 times 10 to the positive 11th and make sure we square it. When we do all this we get a value for the acceleration of the earth that is 5.9019 times 10 to the negative third meters per second per second. We can round that to three significant digits and it becomes 5.90 times 10 to the negative third or 0.00590 meters per second per second.
Solution
5.90 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.