What is the formula for the radius of a satellite's orbit?

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In summary, the correct formula to use in this problem is F=GM/r^2, where F is the given gravitational force, G is the gravitational constant, M is the mass of the Earth, and r is the radius of the satellite's orbit. By plugging in the values given in the problem and solving for r, the radius of the orbit is found to be approximately 8068.29466 kilometers. The formula used is based on Newton's law of gravitation, which relates gravitational force to mass and distance.
  • #1
jacob117
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Homework Statement


A 129 kg satellite experiences a gravitational force by the Earth of 790 N. What is the radius of the satellite's orbit?


Homework Equations


F=GM/R^2


The Attempt at a Solution

 
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  • #2
For an object of mass m under the effect of Earth's gravitational pull, the force pulling it towards the center of the Earth is of a magnitude:

|Fgravity| = m((GMearth)/r²)
where r is the distance of the object from the center of the earth.

Another formula you'll find helpful if there are any follow-up questions is the following:
An object in simple circular motion around a fixed point, is being pulled towards the center of its orbit by a force of magnitude:
|Fcentripetal| = mv²/r
Where v is the tangential speed of the object, and r is the radius of its circular orbit.

Please make an attempt at the solution before asking us to help.
 
Last edited:
  • #3
r^2=G(m1m2)/F
r^2=6.67x10^-11(129x5.98x10^24)/790
r^2=6.67x10^-11(7.7142x10^26)/790
r^2=6.67x10^-11(9.764810127x10^23)
r^2=6.513128355x10^13
r=8070395.501

thats the answer i got but it is still wrong...i need some serious help...
 
  • #4
Final answer is 8068.29466 kilometers, according to Google calculator, so you're in the ball-park. Rounding errors could account for the difference in our answers.
Why do think you're wrong?
 
  • #5
so did i use the proper formula?
 
  • #6
Yes, I think so. But can you explain to me why that was the proper formula?
 
  • #7
hey guys i need some more opinions on this problem...and i just took a guess at the formula...
 
  • #8
jacob117 said:
hey guys i need some more opinions on this problem...and i just took a guess at the formula...

Why do you need more opinions? You got the right answer.

As for why the formula is right, F=Gm1m2/r^2 is Newton's law of gravitation, relating gravitational force to mass and distance. You know F; that was given in the question. You know m1 and m2; one is the mass of the Earth and the other is the astronaut's mass. G is a constant. With one equation and one unknown (r), you can solve for r, which is what the question asks for.
 
  • #9
jacob117 said:
hey guys i need some more opinions on this problem...and i just took a guess at the formula...

Not to sound nitpicky, but RoyalCat gave you the correct formula in Post #2. Your formula in Post #1 was wrong.
 

FAQ: What is the formula for the radius of a satellite's orbit?

How do you find the radius using a ruler?

To find the radius of a circle using a ruler, place the ruler across the center of the circle and measure the distance from one edge to the other. This measurement will be the diameter of the circle, and to find the radius, simply divide the diameter by 2.

What is the formula for finding the radius of a circle?

The formula for finding the radius of a circle is r = d/2, where r is the radius and d is the diameter. This means that the radius is equal to half of the diameter.

Can you find the radius if you only know the circumference?

Yes, you can find the radius if you know the circumference of a circle. The formula for finding the radius using the circumference is r = c/2π, where r is the radius and c is the circumference. This means that the radius is equal to half of the circumference divided by pi (π).

How do you find the radius of a circle using the Pythagorean theorem?

To find the radius of a circle using the Pythagorean theorem, you will need to know the length of the circle's diameter and the distance from the center of the circle to the edge (which is also the radius). Then, you can use the formula r² = (d/2)² - h², where r is the radius, d is the diameter, and h is the distance from the center to the edge.

What is the relationship between the radius and the area of a circle?

The radius and the area of a circle are directly related. The formula for finding the area of a circle is A = πr², where A is the area and r is the radius. This means that as the radius increases, the area of the circle also increases, and vice versa.

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