Keplers law help? (1 Viewer)

[leesh95]

A space shuttle orbiting at an altitude of 270 km orbits Earth exactly 16 times a day. An astronomer observes a satellite passing over her position on ground once every two hours.

calculate the orbital radius of the satellite?

 

[someth1ng]

Silly question.

Orbital Radius=Altitude+Earth's Radius
Orbital Radius=270km+6400km
Orbital Radius=6670km

 

[Parvee]

-16 orbits per day
-One orbit takes 2hrs

interesting...

 

[D94]

A space shuttle orbiting at an altitude of 270 km orbits Earth exactly 16 times a day. An astronomer observes a satellite passing over her position on ground once every two hours.

calculate the orbital radius of the satellite?

Silly question.

Orbital Radius=Altitude+Earth's Radius
Orbital Radius=270km+6400km
Orbital Radius=6670km

-16 orbits per day
-One orbit takes 2hrs

interesting...

I think you guys read the question incorrectly. The space shuttle is not the satellite, from my understanding of the question. Using Kepler’s Law of Periods, instead of applying it to planets orbiting the sun, it's the satellite and space shuttle orbiting the Earth.

You want to use r³/T² = GM/(4∏²) = constant. So, r₁³/T₁² = r₂³/T₂²

So,
r₁ = 270 km + 6380 km
T₁ = 1/(16/day)
r₂ = ? km
T₂ = 1/(12/day)

Edit: Therefore, orbital radius = 8056 km.

 

[clintmyster]

I think you guys read the question incorrectly. The space shuttle is not the satellite, from my understanding of the question. Using Kepler’s Law of Periods, instead of applying it to planets orbiting the sun, it's the satellite and space shuttle orbiting the Earth.

You want to use r³/T² = GM/(4∏²) = constant. So, r₁³/T₁² = r₂³/T₂²

So,
r₁ = 270 km
T₁ = 16/day
r₂ = ? km
T₂ = 12/day (once per 2 hours)

Solving this, you should get 327 km for r₂ (the orbital radius for the satellite).

Good spot, that's right yeah.

 

[leesh95]

I think you guys read the question incorrectly. The space shuttle is not the satellite, from my understanding of the question. Using Kepler’s Law of Periods, instead of applying it to planets orbiting the sun, it's the satellite and space shuttle orbiting the Earth.

You want to use r³/T² = GM/(4∏²) = constant. So, r₁³/T₁² = r₂³/T₂²

So,
r₁ = 270 km
T₁ = 16/day
r₂ = ? km
T₂ = 12/day (once per 2 hours)

Solving this, you should get 327 km for r₂ (the orbital altitude for the satellite).

That is exactly what I got but the answer on the back of the book says 8056 km.

Their working is:
Space shuttle orbital period = 1.5 hours (16/24)

So r1 = 6650?
r2 =
T1= 1.5
T2= 2

And they got 8056 km. I have no idea how they got a radius of 6650 and can't understand their working at all.

 

[leesh95]

Silly question.

Orbital Radius=Altitude+Earth's Radius
Orbital Radius=270km+6400km
Orbital Radius=6670km

That's for the space shuttle. I need to find it for the satellite.

 

[D94]

That is exactly what I got but the answer on the back of the book says 8056 km.

Their working is:
Space shuttle orbital period = 1.5 hours (16/24)

So r1 = 6650?
r2 =
T1= 1.5
T2= 2

And they got 8056 km. I have no idea how they got a radius of 6650 and can't understand their working at all.

Yeah, I was going to make a few corrections (I did it pretty roughly).

For the radius, it should be (6380+270) for the space shuttle, and 6380+A = R for the satellite (A = altitude, R = orbital radius), because it's from the centre of the two masses. (6380 is the radius of the Earth)

The frequency for space shuttle is 16/24, so the period T₁ = 1/f = 1.5, similarly for T₂ = 2.

So using (6380+270) for r₁, you can work out the orbital radius (i.e. the radius of earth + altitude) = 8056 km.

 

[someth1ng]

Yeah, I just read the question again - I quickly read it once...lol, my bad.