Question

A satellite is in a circular orbit around an unknown planet. The satellite has a speed of
1.48 x 10^4
m/s, and the radius of the orbit is 2.26 x 10^6
m. A second satellite also has a circular orbit around this same planet. The orbit of this second satellite has a radius of 9.14 x 10^6
m. What is the orbital speed of the second satellite?
(7360 m/s)
How to get anwser?

Answer 1

\[\left( \frac{ t1 }{ t2 } \right)^2=\left( \frac{ r1 }{ r2 } \right)^3\]
rememeber this equation?

Answer 2

^ its the Kepler's third law equation. T stands for the period

Answer 3

I don't have that equation on my forumla sheet, is there another explanation?

Answer 4

do you want me to explain how i get that equation

Answer 5

this is how you get the equation sorry if it is too big

Answer 6

im not getting the right anwser ,i got 8000, the answer is supposed to be 7360

Answer 7

\[r_1 = 2.26 * 10^6\]\[r_2 = 9.14 * 10^6\]\[C_1=2\pi r_1 =2\pi*2.26*10^6\]\[C_2=2\pi r_2=2\pi*9.14*10^6\]\[v_1=1.48 * 10^4\]\[T_1 = \frac{C_1}{v_1}\]\[T_2=\frac{C_2}{v_2}\]\[v_2=\frac{C_2}{T_2}\]\[(\frac{T_1}{T_2})^2 = (\frac{r_1}{r_2})^3\]\[\frac{\frac{C_1 } {v_1 } } {\frac{C_2 } {v_2 } }=(\frac{r_1}{r_2} )^{3/2}\]\[\frac{C_1 v_2}{C_2 v_1} = (\frac{r_1}{r_2} )^{3/2}\]\[v_2 = (\frac{r_1}{r_2} )^{3/2} \frac{C_2 v_1}{C_1}\]
Plug in the numbers. If you don't make any mistakes, I think you will be happy with the result.