Compare Orbital Speeds of Satellites at Different Altitudes

[lindz.12]

Compare the orbital speeds of satellites that orbit at the following altitudes.
(a) One Earth radius above the surface of the Earth (in km/s)

(b) Two and a half Earth radii above the surface of the Earth.

Here is the equation to be used,

orbital speed is v=(sqrt)(GM/r)
G is the universal gravitational constant
M is the mass of the thing in the middle
r is the distance from the center of the thing in the middle to the center of the thing in orbit.

V=(sqrt) [(6.67E-11)(5.97E24 kg)/ (6378000 m]

...and yet, my answer is incorrect.

 

[LowlyPion]

Welcome to PF.

Aren't the distances they give you above the surface?

Where is the first Earth radius to get to the surface?

 

[mgb_phys]

Those units will give you an answer in m/s, the question asks for km/s

 

[lindz.12]

the distances are what i know...

earth's mass is 5.97E24...whereas its radius is 6378 km...

the answer i got in km/s was 249866.38...which is wrong..and idk why.

 

[mgb_phys]

v = sqrt ( GM/r )
gm = 399 000 km3s-2 for earth, r = 6400km

(a) One Earth radius above the surface of the Earth (in km/s)
So r = 2 * Earth radius,
v = sqrt( 399 000/ (2*6400)) km/s =

(b) Two and a half Earth radii above the surface of the Earth.
So r = 2.5 * Earth radius,
v = sqrt( 399 000/ (3.5*6400)) km/s =

 

[lindz.12]

thank you...but where did you get 399,000? isn't GM 3.98E14??

and also, I'm confused on why the radius is 2 and 3.5...?

 

[mgb_phys]

The question says one Earth radius ABOVE the surface - which is 2 Earth radii from the centre.

GM = 6.674E−11 m^3 kg-^1 s^-2 * 5.97E24 Kg = 3.986 E 14 m^3 s^-2 = 398600 km^3 /s^2

edit - GM comes up a lot in orbital calcs and has an inconveniently large and small value, it's easier to remember that it's about 400,000 (in km and s), or just remember - a bit less than 1/2M (km^3/s^2)

 

[lindz.12]

thanks.