Need help with satellites and Kepler's Laws

In summary, the conversation was about finding the radius of a planet given the mass and period of a satellite in circular orbit around it, along with the magnitude of the gravitational acceleration on its surface. The conversation included various suggestions and equations to solve the problem, until the person was able to figure out the solution using a formula for mass and the equation g=G(M/R^2).
  • #1
fiestytig
7
0
Here's my problem:

A 23.0-kg satellite has a circular orbit with a period of 2.35 h and a radius of 8.90×106 m around a planet of unknown mass. If the magnitude of the gravitational acceleration on the surface of the planet is 8.90 m/s2, what is the radius of the planet?

I got to say, I have no idea where to start since I don't have the mass of the planet. Any help? Pretty please? Due tonight at 10 pm EST... thanks!
 
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  • #2
The force acting on the satellite is also the centripital force. F-mv^2/R and F-G(M*m)/r^2. that should help you find the mass of the planet. right?
 
  • #3
First question: Do you know how to find the period of a satellite if you know the planet's mass and the Radius of its orbit?

Second question: If you do, can't you use this method to find the Planet's mass when you know the period and radius of the orbit?
 
  • #4
I'm afraid I still don't follow, even with those suggestions... All I really know is T^2=4 Pi^2 r^3 /G M. But I don't really have the r either, do I?
 
  • #5
fiestytig said:
I'm afraid I still don't follow, even with those suggestions... All I really know is T^2=4 Pi^2 r^3 /G M. But I don't really have the r either, do I?

Then what is this?

A 23.0-kg satellite has a circular orbit with a period of 2.35 h and a radius of 8.90×106 m around a planet of unknown mass.
 
  • #6
So then how do I find the radius of the planet? (I got confused by the radiuses there for a minute.)
 
  • #7
Aha! I figured it out! Thanks. Had to use a formula to find mass and then use g = G+M/R^2 to find R. :)
 

FAQ: Need help with satellites and Kepler's Laws

What are Kepler's Laws and how do they relate to satellites?

Kepler's Laws are three principles developed by astronomer Johannes Kepler that describe the motion of planets and other celestial bodies around the sun. They also apply to satellites orbiting around a larger body, such as the Earth. The first law states that orbits are elliptical in shape, with the larger body at one focus of the ellipse. The second law states that an object will move faster when closer to the larger body, and slower when farther away. The third law relates the orbital periods of two objects to their distance from the larger body.

How are satellites launched into orbit?

Satellites are launched into orbit using rockets. The satellite is attached to the rocket and carried into space. Once in space, the rocket's engines are used to propel the satellite into its desired orbit around the Earth. The satellite then uses its own propulsion system to make any necessary adjustments to its orbit.

What types of orbits do satellites have?

Satellites can have different types of orbits depending on their purpose. Some common types include low Earth orbit, geostationary orbit, and polar orbit. Low Earth orbit is used for communication and imaging satellites and is around 100-1,200 miles above the Earth's surface. Geostationary orbit is used for weather and communication satellites and is about 22,000 miles above the equator. Polar orbit is used for Earth observation and mapping and orbits over the poles at a lower altitude.

How do satellites stay in orbit?

Satellites stay in orbit due to the balance between their velocity and the force of gravity. The satellite's velocity allows it to move forward at a constant speed, while the force of gravity pulls it towards the Earth. This results in a circular or elliptical orbit around the Earth. In order to maintain this balance, satellites may also use their own propulsion systems to adjust their speed and maintain their orbit.

Can Kepler's Laws be applied to all satellites in the universe?

Yes, Kepler's Laws can be applied to all satellites in the universe, as long as they are orbiting around a larger body. This could include planets orbiting around a star, moons orbiting around a planet, or even artificial satellites orbiting around a planet.

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