How Do You Calculate the Orbital Speed of Satellites?

[Northbysouth]

Homework Statement

Two satellites are in circular orbits around a planet that has radius 9.00x10^6 m. One satellite has mass 65.0kg , orbital radius 6.10×10^7m , and orbital speed 4800 m/s. The second satellite has mass 95.0kg and orbital radius 3.20×10^7m .

Homework Equations

v = sqrt(GM_planet/r)
M_planet = rv^2/G

The Attempt at a Solution

I tried solving for the mass of the plant with the details of the first satellite:

M_planet = (9x10⁶ + 6.10x10⁷)(4800 m/s)²/ (6.67x10^-11)
M = 2.41799x10²⁵ kg

I then used this mass to calculate the speed of the second satellite:

v₂ = sqrt(((6.67x10^-11)(2.41799x10²⁵))/(4.1x10⁷)

v = 2.2489x10³ m/s

 

[voko]

This cannot be correct: the second satellite's orbit is lower, so its speed must be higher.

I suggest that you get a formula that connects speeds and radii symbolically, and then plug in the numbers.

 

[TSny]

Homework Statement

Two satellites are in circular orbits around a planet that has radius 9.00x10^6 m. One satellite has mass 65.0kg , orbital radius 6.10×10^7m , and orbital speed 4800 m/s. The second satellite has mass 95.0kg and orbital radius 3.20×10^7m .


M_planet = (9x10⁶ + 6.10x10⁷)(4800 m/s)²/ (6.67x10^-11)

"Orbital radius" is usually interpreted as the radius of the circular orbit. So, there is no need to add the radius of the planet.

 

[Northbysouth]

I ran the calculation again using v=sqrt(GM/r) with just the orbital radius of the satellite not including the radius of the planet.

Using the first satellite I solved for the mass of the planet:

M_planet = ((6.10x10⁷)(4800²))/(6.67x10^-11)
M = 2.10711x10²⁵

Therefore the speed of the second satellite is:

v = sqrt(((6.67x10^-11)(2.10711x10²⁵))/(3.2x10³)
v = 6.63x10³ m/s

6.63x10³ m/s is the correct answer.