Geostationary Satellite and Orbiting Satellite problem

In summary, the problem requires finding the number of days between January 1 and January 9, for which ComSAT can be directly above point P between 7 PM and 8 PM. Using Kepler's laws, the period of a geostationary orbit with radius RG is 24 hours. Therefore, the period of an orbit with radius 0.81 RG is approximately 23 hours and 56 minutes. To find the number of days, the time needed to make an integer number of orbits between M days and M days plus one hour needs to be determined.
  • #1
agnibho
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0

Homework Statement


A satellite GeoSAT is in a circular geostationary orbit of radius RG above a point P on the equator. Another satellite ComSAT is in a lower circular orbit of radius 0.81RG. At 7 P.M. on January 1, ComSAT is sighted directly above P. On which day among the following can ComSAT be sighted directly above P between 7 P.M. and 8 P.M. ??
(a) Jan 3
(b) Jan 9
(c) Jan 15
(d) Jan 21

2. The attempt at a solution
I am sorry but I am unable to think of any possible way to solve this problem. Will Keplar's equations help?? :confused: I am totally confused! Please help!
For your assistance, the answer given is January 9.
 
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  • #2
What is the period of a geosynchronous orbit with radius RG? Using Kepler's laws, what is the period of an orbit with radius 0.81 RG?
 
  • #3
Umm...would that help?? :/
 
  • #4
agnibho said:
Umm...would that help?? :/

Yes, it will help - that's why I asked the questions. Can you answer them?
 
  • #5
Well, the formula to be applied can be...
T2/R3 = (4 * π2) / (G * M)

where M= 5.98x1024 kg i.e. the mass of the Earth.
Would it help now??
 
  • #6
The above formula is for geosynchronous as I found out... but the question tells about geostationary orbit...
 
  • #7
agnibho said:
The above formula is for geosynchronous as I found out... but the question tells about geostationary orbit...
Geosynchronous and geostationary really mean the same thing. Do you know what a geostationary orbit is? If you do, you should be able to tell me the period of a geostationary orbit without doing any calculations.
 
  • #8
As Wikipedia states, the time period can be
T = 2π √(r3/μ)

What say??
 
  • #9
okay
 
  • #10
phyzguy said:
Geosynchronous and geostationary really mean the same thing. Do you know what a geostationary orbit is? If you do, you should be able to tell me the period of a geostationary orbit without doing any calculations.

Yeah it's 24 hours! :tongue:
 
  • #11
agnibho said:
Yeah it's 24 hours! :tongue:

OK, good. It's actually 23 hours and 56 minutes, but 24 hours is probably close enough. So if the period of the satellite at radius R = RG is T = 24 hours, and if we know from what you wrote earlier that
[tex]\rm \frac{T^2}{R^3} = constant[/tex]
then what is T when R = 0.81RG?
 
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  • #12
You don't need to know M or G. What you need to do is to answer phyzguy's questions.

What's the period of a geostationary satellite?
What do Kepler's laws say about the period of a satellite? Hint: Only one law says anything about the period.

From that, what is the period of that satellite whose orbital radius is 0.81 RG?
 
  • #13
oh okay got it now... so all I have to do is to find out the periods for both the satellites and then calculate the time difference to get the number of days, right?
 
  • #14
agnibho said:
oh okay got it now... so all I have to do is to find out the periods for both the satellites and then calculate the time difference to get the number of days, right?

Right.
 
  • #15
agnibho said:
oh okay got it now... so all I have to do is to find out the periods for both the satellites and then calculate the time difference to get the number of days, right?
There's more to it than that. The satellite will be directly overhead after an integral number of orbits.

Here's what you need to solve for: For what integers N is the time needed to make N orbits between M days and M days plus one hour, where M is another integer?
 

1. What is the difference between a geostationary satellite and an orbiting satellite?

A geostationary satellite is placed in a specific orbit around the Earth that allows it to maintain a fixed position above a certain point on the planet's surface. This means that the satellite appears to be stationary from the perspective of an observer on Earth. An orbiting satellite, on the other hand, follows a path around the Earth and does not remain fixed in one position.

2. How do geostationary satellites stay in orbit?

Geostationary satellites stay in orbit by balancing the gravitational force of the Earth with their forward momentum. They are placed in an orbit around the Earth where the centripetal force of their orbital speed is equal to the gravitational force pulling them towards the Earth. This allows them to maintain a constant distance and position above the Earth's surface.

3. What types of orbits are used for geostationary satellites?

The most common type of orbit used for geostationary satellites is the geosynchronous orbit, where the satellite's orbital period matches the rotation period of the Earth. This allows the satellite to remain above the same point on the Earth's equator. Other types of orbits used include the Molniya orbit, which is highly elliptical and allows for coverage of high latitudes, and the tundra orbit, which provides coverage of polar regions.

4. What are the advantages of using geostationary satellites?

Geostationary satellites have several advantages, including their fixed position above the Earth's surface, which allows for continuous coverage of a specific area. This makes them ideal for applications such as weather forecasting, telecommunications, and television broadcasting. They also have a longer lifespan compared to other types of satellites, as they require less fuel to maintain their orbit.

5. What are some challenges associated with geostationary satellites?

One of the main challenges of geostationary satellites is their limited coverage area. Since they remain fixed above a specific point on the equator, they cannot provide coverage to polar regions or areas with high latitude. They are also susceptible to interference from weather conditions, such as heavy rain or cloud cover. Additionally, the cost of launching and maintaining a geostationary satellite is high, making them less accessible for smaller companies or organizations.

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