Radius of synchronous satellite from a planet

In summary, the conversation discusses the calculation of the distance above the surface of a planet similar to Jupiter where a synchronous satellite must be placed in orbit. The solution involves converting the planet's rotation period to seconds, using Kepler's 3rd law, and subtracting the planet's radius from the final answer.
  • #1
galuda
20
0
[SOLVED] radius of synchronous satellite from a planet

Homework Statement


A "synchronous" satellite, which always remains above the same point on a planet's equator, is put in orbit about a planet similar to Jupiter. This planet rotates once every 7.8h, has a mass of 1.8e27kg and a radius of 6.99e7. Given that G = 6.67e-11 calculate how far above jupiter's surface the satellite must be.


Homework Equations


Kepler's 3rd law


The Attempt at a Solution


well I converted the 7.8 hours to seconds which was 28080 seconds, then did (28080^2*g*1.8e27)/4pi^2, then took the cube root of all that. However that's not right. Any ideas?
 
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  • #2
The expression you used yields the distance between the center the planet and the satellite. You were asked for the height of the satellite above the surface to the planet.
 
  • #3
oh so I just need to subtract the planet's radius from my answer?
 
  • #4
yes that worked thank you very much
 
  • #5
You're welcome.
 

FAQ: Radius of synchronous satellite from a planet

What is the definition of the radius of a synchronous satellite from a planet?

The radius of a synchronous satellite from a planet is the distance between the center of the planet and the orbit of the satellite. It is also known as the orbital radius or the altitude of the satellite.

How is the radius of a synchronous satellite from a planet calculated?

The radius of a synchronous satellite from a planet is calculated using the formula r = (GMT^2)/(4π^2)^(1/3), where G is the gravitational constant, M is the mass of the planet, and T is the orbital period of the satellite.

What is the significance of the radius of a synchronous satellite from a planet?

The radius of a synchronous satellite from a planet is important because it determines the stability and speed of the satellite's orbit. It also plays a role in communication and navigation systems, as satellites in synchronous orbit can remain above the same location on the planet's surface.

How does the radius of a synchronous satellite from a planet affect its gravitational force?

The gravitational force between a planet and its synchronous satellite is inversely proportional to the square of the distance between them. This means that as the radius of the satellite increases, the gravitational force decreases. However, the orbital speed of the satellite also decreases, resulting in a balance that keeps the satellite in its synchronous orbit.

Can the radius of a synchronous satellite from a planet change?

Yes, the radius of a synchronous satellite from a planet can change due to various factors such as atmospheric drag, gravitational pull from other objects, or adjustments made by ground controllers. However, these changes are typically small and carefully monitored to maintain the stability of the satellite's orbit.

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