You know M(r) = v^2r /G
d = distance; s= speed
Planet 1: d=2/s=120
Planet 2: d=4/s=60
Planet 3: d=9/s=40
Planet 4: d=16/s=30
Planet 5: d=36/s = 20
You use the distance and orbital speed of the first planet to determine the mass enclosed within the orbit of the first planet to be 3 solar masses. Do the same thing for the other planets - determining the mass inside the orbits.Figure out how many times bigger/smaller the mass inside the second/third/fourth/fifth orbit is compared to the mass inside the first orbit.
What is d? What is s?
d is distance and s is speed
To determine the mass enclosed within each planet's orbit, we can rearrange the equation M(r) = v^2r / G to solve for mass (M). Here are the steps to find the mass inside each orbit:
1. Planet 1:
We are given that the distance (d) is 2 and the speed (s) is 120. Substitute these values into the equation:
M(2) = (120^2 * 2) / G
2. Planet 2:
The distance (d) is 4 and the speed (s) is 60. Substitute these values into the equation:
M(4) = (60^2 * 4) / G
3. Planet 3:
The distance (d) is 9 and the speed (s) is 40. Substitute these values into the equation:
M(9) = (40^2 * 9) / G
4. Planet 4:
The distance (d) is 16 and the speed (s) is 30. Substitute these values into the equation:
M(16) = (30^2 * 16) / G
5. Planet 5:
The distance (d) is 36 and the speed (s) is 20. Substitute these values into the equation:
M(36) = (20^2 * 36) / G
Now, to compare the mass inside each orbit with the mass inside the first orbit, divide the mass of each planet's orbit by the mass inside the first orbit:
Mass Ratio for Planet 2 = Mass inside Planet 2 orbit / Mass inside Planet 1 orbit
Mass Ratio for Planet 3 = Mass inside Planet 3 orbit / Mass inside Planet 1 orbit
Mass Ratio for Planet 4 = Mass inside Planet 4 orbit / Mass inside Planet 1 orbit
Mass Ratio for Planet 5 = Mass inside Planet 5 orbit / Mass inside Planet 1 orbit
By calculating these ratios, we can determine how many times bigger or smaller the mass inside each orbit is compared to the mass inside the first orbit.