Oribital Speed of a Satellite

[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.

 

[Nickie]

In conclusion, the orbital speed of the second satellite is approximately 2248.9 m/s. This calculation assumes that the planet is not rotating and that the two satellites are in circular orbits. Other factors such as the planet's rotation and the eccentricity of the orbits may affect the actual orbital speed. Additionally, this calculation only takes into account the gravitational force between the planet and the satellite and does not consider any other forces that may affect the satellite's motion.