Determining speed of orbiting object

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In summary: It has the mass of the Earth and the mass of a small object that is orbiting the Earth at the same distance.In summary, the object would have to travel at a speed of 8 km/s to orbit the Earth just at its surface.
  • #1

Homework Statement


The Earth has a radius of approximately 6400 km. If an object could orbit the Earth just at its surface, how fast would it have to travel?

Homework Equations


C = 2πr; ac=v2/r; Fc=mv2/r

The Attempt at a Solution


Circumference = 12800π. I tried to solve for the rate by d = r x t (86400s = 24 hours) but my answer is very small.
 
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  • #2
brake4country said:
I tried to solve for the rate by d = r x t
So I suppose you used the time it takes the Earth to rotate (the time of 1 day). If so then what you calculated is actually the speed with which WE are moving relative to the center of Earth right now. But there's no reason an orbiting object should take the same time to complete one cycle. (If it did happen to take the same time, then we would feel weightless!)

brake4country said:

Homework Equations


Fc=mv2/r
This is the force that is required in order to travel in a circle of radius r at a speed of v
In the case of an object orbiting, what is the source of the centripetal force?
 
  • #3
The source of the centripetal force is the gravitational force from the earth. But no mass was given!
 
  • #4
brake4country said:
The source of the centripetal force is the gravitational force from the earth. But no mass was given!
Hmm... Does gravitational acceleration depend on mass?
brake4country said:
ac=v2/r
 
  • #5
Oh, I see: Fg=Fc
GMm/r2 = mv2/r
GM/r = v2
(6.67x10^-11)(6x10^24)/(6.4x10^6) = 7907.6 m/s or 8 km/s
 
  • #6
brake4country said:
Oh, I see: Fg=Fc
GMm/r2 = mv2/r
GM/r = v2
(6.67x10^-11)(6x10^24)/(6.4x10^6) = 7907.6 m/s or 8 km/s

To answer your question, gravitational acceleration of objects does not depend on mass but I needed the mass of the Earth to calculate this one. The problem did not give it. Am I to know the mass of the earth?
 
  • #7
Hmmm. I just realized that I could have just used mg = mv2/r since the orbital is very close to the surface. Blah!
 
  • #8
brake4country said:
Hmmm. I just realized that I could have just used mg = mv2/r since the orbital is very close to the surface. Blah!
Right. :)

I had the same thought, "if they tell you the radius of Earth, they ought to tell you the mass also!" but then I soon realized that you can just use g=9.8 o0)
 
  • #9
Treat the orbiting mass as negligible (which it is, compared to the earth)
Have a look at the attached sheet.
 

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1. What is the speed of an orbiting object?

The speed of an orbiting object depends on its distance from the object it is orbiting and the mass of the object it is orbiting around. The closer the object is to the center of the orbit, the faster it will travel.

2. How do you calculate the speed of an orbiting object?

To calculate the speed of an orbiting object, you can use the formula v = √(GM/r), where v is the speed, G is the gravitational constant, M is the mass of the object being orbited, and r is the distance between the two objects.

3. Does the shape of the orbit affect the speed of an object?

Yes, the shape of the orbit can affect the speed of an object. For example, in a circular orbit, the speed remains constant, while in an elliptical orbit, the speed will vary depending on the distance from the object being orbited.

4. How can we measure the speed of an orbiting object?

The speed of an orbiting object can be measured using various methods such as radar, telescopes, and spacecraft. These methods use the principles of distance and time to determine the speed of the object.

5. What units are used to measure the speed of an orbiting object?

The speed of an orbiting object is usually measured in kilometers per second (km/s) or meters per second (m/s). However, it can also be measured in miles per hour (mph) or kilometers per hour (km/h).

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