Finding the radius in the universal gravity equation

In summary, the student is trying to find the radius of an orbit and is stuck because they don’t know what equations to use or how to solve for the unknowns.
  • #1
Madelin Pierce
24
2

Homework Statement


G= 6.67 *10^-11
M= 5.97*10^24 kg
m= 430 kg
Orbital speed=6800m/s
I'm supposed to find radius of satellite orbit.

Homework Equations

The Attempt at a Solution


I don't know where to start because in order to find radius, I have to find period as well
 
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  • #2
Assuming a circular orbit, what force is providing the centripetal force to maintain that circular motion?

What equations are relevant?
 
  • #3
Fg= G*M*m/r^2, v=2Pi(r)/T, acent=v^2/r
I'm not sure what force maintains circular motion. I would assume gravity
 
  • #4
Madelin Pierce said:
Fg= G*M*m/r^2, v=2Pi(r)/T, acent=v^2/r
I'm not sure what force maintains circular motion. I would assume gravity
Gravity is correct. It's providing the centripetal force.

There's an equation for centripetal force that involves the velocity but not the period T. Do you know what it is?
 
  • #5
I don't think so. I know there's F=mv^2/r, but I would still have two unknowns, Fg and r.
 
  • #6
Madelin Pierce said:
I don't think so. I know there's F=mv^2/r, but I would still have two unknowns, Fg and r.

Do you have an expression for gravitational force? (I assume that's what you mean by Fg.)
 
  • #7
Madelin Pierce said:
I don't think so. I know there's F=mv^2/r, but I would still have two unknowns, Fg and r.
Yes. That's good for ##F_c##. You've already stated an equation for ##F_g##. Try equating them. Can you solve for r?
 
  • #8
Madelin Pierce said:
I don't think so. I know there's F=mv^2/r, but I would still have two unknowns, Fg and r.

Everybody keeps asking if you have equations that you already wrote!

You said the centripetal force must be
F = mv^2/r

You said the gravitational force is
Fg = G Mm/r^2

When asked what force maintains orbit you said “I assume gravity”

You said “I would still have 2 unknowns”

So that’s 2 equations in 2 unknowns. Hmmm ... what to do, what to do?
 

1. What is the universal gravity equation?

The universal gravity equation, also known as Newton's Law of Universal Gravitation, is a mathematical formula that describes the gravitational force between two objects. It states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

2. How do you find the radius in the universal gravity equation?

To find the radius in the universal gravity equation, you can use the formula r = (GM)/(F), where r is the radius, G is the gravitational constant, M is the mass of the larger object, and F is the force of gravity between the two objects. You can also rearrange the equation to solve for the radius by dividing the force by the product of the masses and then taking the square root.

3. What is the role of the radius in the universal gravity equation?

The radius in the universal gravity equation represents the distance between the two objects. This distance is a crucial factor in determining the strength of the gravitational force between the two objects. The larger the distance between the objects, the weaker the force of gravity will be.

4. Can the radius in the universal gravity equation be negative?

No, the radius in the universal gravity equation cannot be negative. This is because the distance between two objects can never be negative. However, the force of gravity can be negative if the two objects are moving in opposite directions, but this does not affect the radius in the equation.

5. What are some real-life applications of the universal gravity equation?

The universal gravity equation is used in many areas of science and engineering, including space exploration, rocket trajectory calculations, and satellite orbits. It is also used in many everyday situations, such as calculating the weight of an object on Earth or determining the gravitational pull between the Earth and the Moon.

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