Finding ortibal period and orbital speed PLEASE HELP

In summary, finding the orbital period and orbital speed of an object involves using Kepler's Third Law and the equations for orbital velocity and centripetal force. The orbital period, or time it takes for an object to complete one orbit, is determined by the object's distance from the central body and the mass of the central body. The orbital speed, or velocity of the object, is dependent on the same factors and can be calculated using the equation for centripetal force. By understanding these laws and equations, scientists are able to accurately calculate and predict the orbital characteristics of objects in space.
  • #1
mandi_babe1
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Homework Statement


GPS (Global Positioning System) satellites orbit at an altitude of 2.6×107 .
Find the orbital period.
Find the orbital speed of such a satellite.


Homework Equations


I would like to know how to approach this. I don't know where to start w/o other figures.


The Attempt at a Solution


I went through a long, convoluted process and determined 2.8*10^29, which is entirely wrong. Please help!
Thank you in advance!
 
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  • #2

1. How do you calculate orbital period?

The orbital period of an object can be calculated using the formula T = 2π√(a^3/GM), where T is the orbital period in seconds, a is the semi-major axis of the orbit in meters, G is the universal gravitational constant (6.67 x 10^-11 Nm^2/kg^2), and M is the mass of the central object in kilograms.

2. What is orbital speed?

Orbital speed refers to the velocity at which an object is moving in its orbit around a central object. It is calculated using the equation v = √(GM/r), where v is the orbital speed in meters per second, G is the universal gravitational constant, M is the mass of the central object, and r is the distance between the object and the central object.

3. Can orbital period and orbital speed change?

Yes, both orbital period and orbital speed can change depending on the factors that affect them. For example, if the mass of the central object changes, the orbital speed will also change. Similarly, if the semi-major axis of the orbit changes, the orbital period will also change.

4. How does the mass of the central object affect orbital period and speed?

The mass of the central object has a direct effect on both orbital period and speed. As the mass increases, the orbital speed increases, and the orbital period decreases. This is because the greater the mass, the stronger the gravitational pull between the objects, resulting in a faster orbital speed and a shorter orbital period.

5. Can you use the same formula to calculate orbital period and speed for all objects?

No, the formula for calculating orbital period and speed may vary depending on the specific characteristics of the objects in question. For example, the formula for calculating orbital period for a planet orbiting a star will be different from the formula for calculating orbital period for a moon orbiting a planet. It is important to use the correct formula for each unique scenario.

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