You have just discovered a planetary system consisting of a star (Dagobahr) and its two planets: Rool and Krau. Planet Rool has an average orbital radius 3 times as big as planet Krau. If planet Rool orbits Dagobahr in 2 earth years (1earth year = 365 days).
a) how long is the year for the residents of Krau? (in earth years, days and seconds.
Would I use (T_K/T_R)^2 =(r_K/r_R)^3
(T_K/2 years)^2 = (1/3)^3
T_k= .385 earth years
=140.5 days
=12,139,200 seconds
b)What is the average linear orbital velocity of Krau if Rool has an average orbital radius of R_RD=3x10^11m?
T=(2 * pi * r)/v
c) find the average value of Krau's centripetal acceleration in its orbit around Dagobahr.
a_c= v_K^2/r_K
d) find the average value of the centripetal force exerted by Dagobahr on Krau. (mass of Krau = 2x10^24kg).
F_c= (M_K * v_K^2)/r
(What would be the radius of Krau? would it be 3x10^11 divided by 3?)
e) what is the average gravitational force exerted by Dagobhr on Krau?
g=(G * M_k)/r
f) what is the average gravitational force exerted by Krau on Dagobahr?
(aren't e) and f) the same answers?)
g) Mass of Dagobahr?
g_D=(G * M_D)/r^2
(where g_D is from problem e))
h) what is the angular velocity of Krau in radians per day?
v=rw so thus w=v/r
i ) what is the angular momentum of Krau?
L=Iw
and I=mr^2
I just wanted to know if this is correct otherwise if I don't get parts a) b) c) ect. right the rest will be wrong. Thanks in advance for your help.
b, figure v, not T.
c. yes
d, yes
e. Don't do it that way. The gravitational force has to be equal to the centripetal force.
f. Ok.
g. yes
h. yes.
Yes means the correct method.