Dot Point Physics Prep (1 Viewer)

[Tacoo]

Can anyone help me with question 2.14.3 under space? I figured part (a) but I'm stuck with part (b)

2.14.3 Three moon around planet X have masses M, 9 M and 16 M.

(a) If all moons are the same distance from the planet's centre, calculate the ratio of their orbital speeds.
Easy, 1:1:1, orbital speed is independent of mass

(b) If the distances of these moons from the planet's centre are R, 9 R and 16 R respectively, calculate the ratio of their orbital speeds


Pls halp

 

[superSAIyan2]

orbital velocity = root (GX/r) where X is the planets mass (didnt wanna use M since question used it)
For planet with radius R
Orbital velocity = root (GM/R)
For planet with radius 9R
orbital velocity = root( GM/9R) = 1/3 root (GM/R)
for planet with radius 16R
orbital velocity is 1/4 root (GM/R)

thus ratio is 1 : 1/3 : 1/4 ---> 12:4:3

 

[Tacoo]

orbital velocity = root (GX/r) where X is the planets mass (didnt wanna use M since question used it)
For planet with radius R
Orbital velocity = root (GM/R)
For planet with radius 9R
orbital velocity = root( GM/9R) = 1/3 root (GM/R)
for planet with radius 16R
orbital velocity is 1/4 root (GM/R)

thus ratio is 1 : 1/3 : 1/4 ---> 12:4:3

ahhh makes sense, so for GM, the value is 1?, so root (1/1) = 1 or root (1/9) = 1/3?

 

[superSAIyan2]

the GM's cancel out