Altitude of Satellites above the Surface of the Earth

In summary: Oh! I think I get it! I am so sorry for not understanding it earlier. So they both do have the same orbital period, but the altitude of each satellite is different because they are moving at different speeds, and the Earth's rotation also affects their positions in the sky. So, to summarize, the first satellite has an altitude of 35846910.18m and the second satellite has an altitude of 42226910.15m. In summary, the two satellites have the same orbital period but different altitudes due to their different speeds and the Earth's rotation. The first satellite has an altitude of 35846910.18m and the second satellite has an altitude of 42226910.15
  • #1
Bassa
46
1

Homework Statement



A) Suppose you are on Earth's equator and observe a satellite passing directly overhead and moving from west to east in the sky. Exactly 12.0 hours later, you again observe this satellite to be directly overhead. How far above the Earth's surface is the satellite's orbit?

B) You observe another satellite directly overhead and traveling east to west. This satellite is again overhead in 12.0 hours. How far is this satellite's orbit above the surface of the earth?[/B]

Homework Equations


T=(2πr^3/2)/(√Gm)

The Attempt at a Solution


Well, I thought that they would both have the same altitude since they have the same period. This is evidently not correct since the back of the book has two different answers for A and B.

I plugged in the numbers for the variables. I dropped the units. I would have looked very messy.

86400=(2πr^3/2)/(√(6.67x10^-11)(5.97x10^24))

I solved for r

r=42226910.15m

altitude= r-Re=35846910.18m which matched what the book has as an answer for B, but why is this the answer for B. Why would they both have different altitude if they have the same period, but in opposite direction? May I get any hint for part A and some clarification on part B?
 
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  • #2
What makes you think they have the same period?
 
  • #3
voko said:
What makes you think they have the same period?
Well, from the description in the problem, I thought that they were both geosynchronous satellites. If so, would not that make them have the same period? The only difference would be that one is going in the direction of the Earth's rotation and the other is going in the opposite direction.
 
  • #4
Bassa said:
Well, from the description in the problem, I thought that they were both geosynchronous satellites.

Really? How is the geosynchronous orbit defined?
 
  • #5
Why would they be geosynchronous? Clearly they are not geosyncronous because they are not stationary relative to a geographical location on the Earth.
 
  • #6
the Earth is spinning counter-clockwise about its axis, so you must take that into account
 
  • #7
voko said:
Really? How is the geosynchronous orbit defined?
A geosynchronous orbit is an orbit in which the satellite is locked over one place relative to the earth. The Earth and the satellite would have the same orbital velocity. On a second thought, I don't see a lot of evidence to support the geosynchronous orbit hypothesis. They may have fast orbital velocity that would allow them to appear again on the same spot after a given time interval.
 
  • #8
You (the observer) are orbiting the Earth with angular speed one revolution per day. What angular speeds must the satellites have so that your angular positions and theirs overlap twice a day?
 
  • #9
Suppose you know a person is walking with velocity v. If the person and you are both moving toward each other, could you say that the person's absolute velocity is just v?
 
  • #10
Jazz said:
Suppose you know a person is walking with velocity v. If the person and you are both moving toward each other, could you say that the person's absolute velocity is just v?

No, it would be his relative velocity to me.
 
  • #11
v would be the velocity relative to an observer at rest. It would be different if the observer is not so.

In the problem, you don't have a inertial frame of reference. You must figure out their absolute velocities.

If you had a geosynchronous satellite right over you, you would say that it's not moving at all, but that is not the case.
 
  • #12
Jazz said:
v would be the velocity relative to an observer at rest. It would be different if the observer is not so.

In the problem, you don't have a inertial frame of reference. You must figure out their absolute velocities.

If you had a geosynchronous satellite right over you, you would say that it's not moving at all, but that is not the case.

What indicates to us that it is not geosynchronous?
 
  • #13
The satellites appear directly above the observer at the initial time and 12 hours later, but not in between. That rules out geostationary satellites (it would also make "move east to west" and "west to east" wrong).

How does the position of the observer on Earth (relative to a non-rotating frame) change during 12 hours?
 
  • #14
mfb said:
The satellites appear directly above the observer at the initial time and 12 hours later, but not in between. That rules out geostationary satellites (it would also make "move east to west" and "west to east" wrong).

How does the position of the observer on Earth (relative to a non-rotating frame) change during 12 hours?

So, after completing half a period on earth, the satellite appears again. Does that mean that the satellite completed 1.5 times the period of the earth?
 
  • #15
Bassa said:
What indicates to us that it is not geosynchronous?

If I have the means to view a geosynchronous satellite, I would be able to view it whenever I want and I'd find it always in the same place in the sky.

If this doesn't happen, then it's not a geosynchronous satellite.
 
  • #16
Bassa said:
So, after completing half a period on earth, the satellite appears again. Does that mean that the satellite completed 1.5 times the period of the earth?
What does "1.5 times the period of the earth" mean? The number 1.5 is correct for one of the satellites, I'm not sure if the interpretation is correct as well.
 
  • #17
mfb said:
What does "1.5 times the period of the earth" mean? The number 1.5 is correct for one of the satellites, I'm not sure if the interpretation is correct as well.

Sorry for not being very clear. I meant that the satellite must have circled the Earth 1.5 times for it to satisfy the information of when it was observed the second time. When it was spotted the first time in situation A, it was not seen in the sky until 12 hours later. This means that the satellite passed the point at witch it was spotted the first time. It was heading toward the east then it came back to the original spot in the sky when it was first observed, but the observer was already gone due to the rotation of the earth. Then, when it continued going around the earth, it reached the point where the observer is at. This happened twelve hours later of when it was originally observed.
 
  • #18
So what is the period of the satellite that makes 1.5 revolutions when the Earth does 0.5?
 
  • #19
voko said:
So what is the period of the satellite that makes 1.5 revolutions when the Earth does 0.5?
according to my calculations it should be 8.0 hours or 28800 seconds. This is for situation A.
 
  • #20
What about B?
 
  • #21
voko said:
What about B?

I think I am going to finish part A first and then move to part B. ^-^
 
  • #22
voko said:
What about B?

My next move is to use T=2pi(r^3/2)/sqrt(GMe)
Me= mass of the earth
T= period of the satellite
Am I in the right direction?
 
  • #23
Yes, that seem OK.
 
  • #24
voko said:
What about B?

Now, for B its period is the same as the period of the earth. This mean that the same method will apply, but I would have to use 24 86400 seconds for the period in my formula. Does that sound okay? I used a solar system mobile that my girlfriend got me so I could wrap my head around it. I wonder if I am allowed to take the mobile with to a test. ^_^
 
  • #25
Same period as the period of the Earth is correct, but what is 24 86400 seconds?

You do not need a mobile to understand this. Take your girlfriend instead, draw a circle in the ground, and have fun.
 
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  • #26
voko said:
Same period as the period of the Earth is correct, but what is 24 86400 seconds?

You do not need a mobile to understand this. Take your girlfriend instead, draw a circle in the ground, and have fun.

Sorry, I was going to write 24 hours, but I realize that I need to use the SI unit for time to save me a lot of conversions and prevent me from making mistakes. I forgot to delete it.

This sounds so good at the moment. The weather is very cold where I live. Unfortunately, she lives away from me. She goes to a different college.Next year, I will be going to the college that she currently attends to finish my physics degree.
 
  • #27
Thank you everyone for your help. You guys are amazing. I love how you don't just give us the answer, you direct us to the right path.
 
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1. What is the altitude of satellites above the surface of the Earth?

The altitude of satellites above the surface of the Earth varies depending on the type of satellite and its purpose. For example, communication satellites typically orbit around 22,000 miles above the Earth's surface, while GPS satellites orbit at a distance of approximately 12,500 miles.

2. Why do satellites need to be at a specific altitude?

Satellites are placed at specific altitudes to maintain a stable orbit around the Earth. This is necessary to ensure that the satellite remains in a predictable position for communication, imaging, or other purposes. If the satellite is too low, it may experience atmospheric drag and eventually fall to Earth, while if it is too high, it may escape the Earth's gravitational pull.

3. How do scientists calculate the altitude of satellites?

The altitude of a satellite is calculated using the satellite's orbital period, or the time it takes to complete one orbit around the Earth. This can be determined using Kepler's third law of planetary motion, which relates the orbital period to the satellite's altitude and the mass of the Earth.

4. Can satellites orbit at any altitude?

No, satellites cannot orbit at any altitude. The altitude of a satellite is determined by its purpose and the desired orbit. For example, weather satellites may need to be placed at a lower altitude to capture detailed images of the Earth's surface, while communication satellites may need to be placed at a higher altitude for global coverage.

5. How does the altitude of a satellite affect its speed?

The altitude of a satellite does not affect its speed, but rather its orbital period. Satellites at higher altitudes have longer orbital periods, while those at lower altitudes have shorter orbital periods. This is due to the fact that the gravitational pull of the Earth decreases with distance, so satellites at higher altitudes experience less gravitational force and therefore move at a slower speed.

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