Uniform Circular Motion of a satellite

[Muneerah]

Hi, so I got stuck on this problem and I really don't know what it is that I'm not doing right, so if you can please help me. Thank you

Homework Statement

A satellite is in a circular orbit 11000 km
above the Earth’s surface; i.e., it moves on a
circular path under the influence of nothing
but the Earth’s gravity.

A) Find the speed of the satellite. The radius
of the Earth is 6.37 × 106 m, and the accel-
eration of gravity at the satellite’s altitude is
1.3225 m/s² .
Answer in units of km/s.

B) Find the time it takes to complete one orbit
around the Earth.
Answer in units of s.

Homework Equations

V= 2 pi r / T
a= v^2/r
T= V/ 2 pi r

The Attempt at a Solution

First I found the hypotonus between the Earth and the orbit so I can find the radius of the latitude of the orbit. I got 6370 km. Then I converted the acceleration from m/s² to Km/s² and I got: .0013225 km/s². Then to find the velocity I did
V= ((.0013225)(6370))^(1/2)= 2.902 Km/s

for the time I got 7.2681x10^-5s.

and both answers were wrong.

 

[Chewy0087]

Hi, so I got stuck on this problem and I really don't know what it is that I'm not doing right, so if you can please help me. Thank you

Homework Statement

A satellite is in a circular orbit 11000 km
above the Earth’s surface; i.e., it moves on a
circular path under the influence of nothing
but the Earth’s gravity.

A) Find the speed of the satellite. The radius
of the Earth is 6.37 × 106 m, and the accel-
eration of gravity at the satellite’s altitude is
1.3225 m/s² .
Answer in units of km/s.

B) Find the time it takes to complete one orbit
around the Earth.
Answer in units of s.

Homework Equations

V= 2 pi r / T
a= v^2/r
T= V/ 2 pi r

The Attempt at a Solution

First I found the hypotonus between the Earth and the orbit so I can find the radius of the latitude of the orbit. I got 6370 km. Then I converted the acceleration from m/s² to Km/s² and I got: .0013225 km/s². Then to find the velocity I did
V= ((.0013225)(6370))^(1/2)= 2.902 Km/s

for the time I got 7.2681x10^-5s.

and both answers were wrong.

Hmm, would you kindly explain what you did to "find the hypotenuse"? If you check, you can see that the value you've used for the orbit is the same as the radius which you're given for the earth...?

Surely when finding the radius of the orbit it's simply the radius of the Earth + the distance vertically upwards (which you're told in the question) from the surface? (doesn't yield 6370km!)

 

[Muneerah]

ughh, I feel really stupid, well I tried finding the radius in two different ways. The first one I found the angle of the orbit, which was 80, then used cos80 = r/1100km = 191.01 km. And the second time I found the hyponuse using pythagorean theorem. So the right radius is basically the radius of the Earth + 1100 km ?

 

[Chewy0087]

1100? You mean 11000 right?

But yeah sure. Don't worry I spent a day a while back trying to find the maximum of a function (pretty complex), trying some crazy stuff (alot of division by 0) but then i decided to graph it and realized there wasn't one >.<

 

[Muneerah]

Yes, I got it right. Thank you so much, but I was wondering why do we add the distance traveled upward with the radius of the Earth ??

 

[Chewy0087]

Because that's the total distance which it is away from the centre of the Earth (where the mass of the Earth is said to be).

Look at this (normal circle);

http://upload.wikimedia.org/wikibooks/en/5/51/Radius.jpg

Now if the satellite is in orbit 11000km straight upwards you can simply extend the line labelled r to the relevant distance because by being "straight upward" you're traveling perpendicularly to the surface of the earth, which is why you can simply add up the radius with the distance above the surface.

Do you understand now? It's a simple concept when you get it but I fear I've not explained it very well...