How Does the Mass of the ISS Affect Its Orbital Motion?

[billybobay]

I'm not asking for you to do my homework but can you help me on it?! I have no idea how to even attempt it. Any help would be greatly appreciated!

The International Space Station (ISS) just celebrated its 10th anniversary of human habitation. During that time it has been orbiting the Earth at an altitude of 350 Km.

a. If the radius of the Earth is 6,370 Km, what is the period of orbit for the ISS?
b. Does the orbiting speed of the ISS depend on its mass?
c. Suppose the ISS is in a stable orbit when the space shuttle brings in a new component for attachment. This increases the mass of the ISS. Do the astronauts have to adjust the speed of the shuttle to maintain the same orbit? (hint: momentum is always a factor in our universe) Explain your reason for your answer.
d. If the ISS were to be moved to a geosynchronous orbit (always staying above the same point on the earth), What would the new altitude of the ISS have to be?




2. The attempt at a solution

a. 6370+350=6720 km is the period of orbit? is that correct?
b. I need a lot of help!
c. I need a lot of help!
d. I need a lot of help!

 

[BruceW]

hmmm, if your teacher is setting you this homework, then I guess he/she has already taught you the relevant concepts? The important topics for this question are: Newton's law of universal gravitation, circular motion and centripetal acceleration. look back at your notes, and hopefully it will start to make sense. Also, has your teacher gone through these types of questions in class with you yet?

 

[Bread18]

For a, the orbital period is the time it takes for the object to do 1 complete orbit.

 

[bigfooted]

a) period is the time it takes to complete a circle around the earth. It is in units of time. you just calculated the radius of the orbit, which you will need to calculate the orbital velocity.
Orbital velocity v=sqrt(Gm/r). Do you know G,m and r? When you have the velocity, you can calculate how long it takes to traverse a circle with radius 6720 km.
b) Is the mass of the ISS in the equation for the period?
c) what does the hint mean?
d) When the ISS is always above the same point above the earth, what is the period of the ISS compared to the period of the earth?

 

[asteriatic]

Hello! I understand that you are not asking for me to do your homework, but rather seeking assistance in understanding the concept of orbital motion. I would be happy to provide some guidance and explain the concepts involved in this problem.

a. To find the period of orbit, we can use the formula T^2 = 4π^2 * (r^3/GM), where T is the period, r is the distance between the center of the Earth and the object in orbit, G is the gravitational constant, and M is the mass of the Earth. Plugging in the given values, we get T^2 = 4π^2 * ((6370+350)^3/6.67x10^-11 * 5.97x10^24). Solving for T, we get a period of approximately 5573 seconds, or about 1.55 hours.

b. No, the orbiting speed of the ISS does not depend on its mass. According to Newton's laws of motion, the orbiting speed of an object in orbit is determined by the gravitational force of the larger body (in this case, the Earth) and the distance between the two objects. The mass of the orbiting object does not affect its orbiting speed.

c. When the mass of the ISS increases, the astronauts would need to adjust the speed of the shuttle in order to maintain the same orbit. This is because of the conservation of momentum. When the new component is attached, the overall mass of the ISS increases, which means its momentum also increases. In order to keep the same orbit, the shuttle would need to increase its speed to match the increased momentum of the ISS.

d. To be in a geosynchronous orbit, the ISS would need to have an orbital period of 24 hours, which is the same as the Earth's rotation period. Using the same formula as before, we can solve for the new altitude by setting the period T to 24 hours and solving for r. The new altitude would be approximately 35,786 km above the Earth's surface.

I hope this helps you understand the concepts involved in orbital motion and how to approach this problem. Remember to always use the appropriate formulas and units when solving for these types of problems. Good luck!