Circular and Satellite Motion Legacy Problem #23 Guided Solution
Problem*
Determine the orbital speed of the Earth as it orbits about the Sun. (GIVEN: Msun = 1.99 x 1030 kg and Earth-sun distance = 1.50 x 1011 m)
Audio Guided Solution
According to Newton's Law of Universal Gravitation, the speed of an orbiting satellite, such as the speed of the Earth about the Sun, is dependent upon the mass of the object that is being orbited and the radius of orbit. Here we are given the mass of the Sun, the object that the Earth orbits, and we are also given the mean distance from the Earth to the Sun, 1.5 times 10 to the 11th meters. This would be the radius of orbit, and we would calculate the speed of the Earth orbiting the Sun as the square root of big G times the mass of the Sun divided by the radius of the orbit. We have the big G value being 6.673 times 10 to the negative 11th Newtons meters squared per kilogram squared. We can substitute that in and multiply it by the mass of the Sun and divide by this mean distance between Earth and Sun, and then take the square root of the result. It gives us about 2.98 times 10 to the 4th meters per second.
Solution
2.98 x 104 m/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.