Circular and Satellite Motion Legacy Problem #17 Guided Solution
Problem*
Determine the force of gravitational attraction between the Earth and the moon. Their masses are 5.98 x 1024 kg and 7.26 x 1022 kg, respectively. The average distance separating the Earth and the moon is 3.84 x 108 m. Determine the force of gravitational attraction between the Earth and the moon.
Audio Guided Solution
Newton's Law of Universal Gravitation states that all objects with mass attract with a force which is proportional, directly proportional to the product of their masses, and inversely proportional to the square of the separation distance between them. Applied to this situation of the Earth and the Moon, we can calculate the force of gravitational attraction using the equation F-grab equal big G times the mass of the Earth times the mass of the Moon divided by the separation distance squared. The big G value is 6.673 times 10 to the negative 11th newtons times meter squared per kilogram squared. So using that as the proportionality constant, we can calculate F-grab by going that big number G multiplied by 5.98 times 10 to the 24th multiplied by 7.26 times 10 to the 22nd divided by the quantity 3.84 times 10 to the 8th, that whole thing squared. When we do that, we find the force of gravitational attraction between the Earth and the Moon to be 1.96 times 10 to the 20th newtons. Now if you got a number that was 1.96 times 10 to the something other than 20th newtons, then perhaps you're having difficulty with your calculator as you enter these numbers. My recommendation for entering numbers on your calculator in scientific notation is that you enter a number like 5.98 times 10 to the 24th as 5.98, and then you push the E button, which means exponent base 10. Instead of going 5.98 times 10, E button, which would make your number off by a factor of 10.
Solution
1.96 x 1020 N
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.
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