A planet has two satellite moons. Moon X has an orbital period of 2.13 days. Moon Y has an orbital period of about 3.53 days. Both moons have nearly circular orbits. Use Kepler's third law to find the distance of each satellite from the planet's center. The planet's mass is 2.0 10^26 kg.
Moon X km?
Moon Y km?
I have posted this earlier but didn't get a respond am sorry to re-post it but I really need help with this!
Physics - drwls, Sunday, February 19, 2012 at 12:27pm
The Kepler's law formula you need to use is:
T²/R³ = 4π²/(GM)
M is the mass of the planet, in kg
G is the universal constant of gravity, which is easily found online.
T is the period in seconds
Tx = 1.840*10^5 s
Ty = 3.050*10^5 s
R is the orbit radius in meters. Do the calculations of R for planets X and Y, one at a time.
Ok i tried this but i still cant get the answer right I don't understand it :(
Physics - bobpursley, Thursday, February 23, 2012 at 8:46pm
T^2/R^3=4PI^2/GM
R= cubrt ( T^2 G*mass/4PI^2)
solve for R, knowing period T, G, Mass.
Do that for each moon.
Physics - Angelina, Thursday, February 23, 2012 at 9:00pm
Ok so this is what i did cubrt(2.13^2(6.67x10^-11)(2.0x10^26))/(4pi2)=R which is 1159307512 but then that's wrong so i don't know what i am doing wrong?
To find the distance of each satellite from the planet's center, you can use Kepler's Third Law. The formula is:
T^2 / R^3 = 4π^2 / (GM)
where T is the orbital period of the satellite, R is the distance of the satellite from the planet's center, G is the universal gravitational constant (about 6.67 x 10^-11 N m^2/kg^2), and M is the mass of the planet.
Let's solve for Moon X first:
- The orbital period of Moon X is 2.13 days, which is equivalent to 1.840 x 10^5 seconds.
- Plug in the values into the formula:
(1.840 x 10^5)^2 / R^3 = 4π^2 / (6.67 x 10^-11 x 2.0 x 10^26)
- Rearrange the formula to solve for R:
R = (1.840 x 10^5)^2 / cuberoot(4π^2 / (6.67 x 10^-11 x 2.0 x 10^26))
- Calculate the value of R using a scientific calculator.
Now let's solve for Moon Y:
- The orbital period of Moon Y is 3.53 days, which is equivalent to 3.050 x 10^5 seconds.
- Plug in the values into the formula:
(3.050 x 10^5)^2 / R^3 = 4π^2 / (6.67 x 10^-11 x 2.0 x 10^26)
- Rearrange the formula to solve for R:
R = (3.050 x 10^5)^2 / cuberoot(4π^2 / (6.67 x 10^-11 x 2.0 x 10^26))
- Calculate the value of R using a scientific calculator.
Remember to convert the resulting values of R from meters to kilometers by dividing by 1000.
By following these steps, you should be able to find the distance of each satellite from the planet's center.