Planetary Motion, calculation of orbital period

In summary, a question is asked about calculating the orbital period of a space shuttle orbiting the Earth with given information. The correct equation is provided, but the asker wonders why they can't use another equation. The responder explains that the other equation is a constant and does not have the same dimensions as the gravitational field strength.
  • #1
Stevo_evo_22
2
0
Hi everyone,



I'm really confused with a particular question:

Homework Statement






A space shuttle orbits the Earth at 6720 km from its centre. The gravitational field strength is 8.9N/kg. Calculate the shuttle's orbital period in minutes...

Homework Equations



g=4pi^2 x R /T^2

The Attempt at a Solution


The thing is, I know how to solve it using g=4pi^2 x R /T^2, but I want to know why I can't just use g=r^3/T^2 (the constant for all objects orbiting a particular mass)...if I have r and g, why can't i just use this equation?

Thanks!

Steve
 
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  • #2
Because r^3/T^2 is a constant. But that constant isn't the same as g. It doesn't even have the right dimensions.
 
  • #3
Dick said:
Because r^3/T^2 is a constant. But that constant isn't the same as g. It doesn't even have the right dimensions.

ahh ok...thanks :)
 

Related to Planetary Motion, calculation of orbital period

1. What is planetary motion?

Planetary motion refers to the movement of planets in their orbits around the sun. These orbits are elliptical in shape, with the sun located at one of the foci.

2. How is the orbital period of a planet calculated?

The orbital period of a planet can be calculated using Kepler's third law, which states that the square of a planet's orbital period is directly proportional to the cube of its average distance from the sun. This can be expressed as T2 = (4π2 / G) x a3, where T is the orbital period, G is the gravitational constant, and a is the semi-major axis of the planet's elliptical orbit.

3. What factors affect the orbital period of a planet?

The orbital period of a planet can be affected by its distance from the sun, the mass of the planet, and the gravitational force exerted by other celestial bodies. The greater the distance from the sun and the larger the mass of the planet, the longer the orbital period will be. Additionally, the presence of other planets or moons can also affect the orbital period.

4. Can the orbital period of a planet change over time?

Yes, the orbital period of a planet can change over time due to factors such as interactions with other celestial bodies, changes in the planet's mass or orbit, and the influence of external forces such as solar winds. However, these changes are typically very small and can only be detected through precise observations and calculations.

5. How is the concept of orbital period related to the concept of time?

The orbital period of a planet is directly related to the concept of time. It is the time it takes for a planet to complete one full orbit around the sun. Therefore, the orbital period is a fundamental unit of measurement for defining time in the context of our solar system.

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