# Gravity and Orbital Velocity: Understanding a Common Misconception

• momoneedsphysicshelp
In summary: Velocity is independent of mass, radius is the same for both. In summary, the conversation discusses the problem of two satellites in the same circular orbit around the Earth and the statement that the speed of the satellites is independent of mass. The correct answer is B, but the instructor marked it incorrect, possibly due to a misunderstanding of the question. The conversation also includes a discussion of the relevance of knowing the orbital radius in comparing the speeds of the satellites.
momoneedsphysicshelp
Homework Statement
Two satellites are in the same circular orbit around the Earth. Satellite A has mass of m and satellite B mass of 2m. Which one of the following statements is true about the speeds of these satellites?
Relevant Equations
A: satellite A's velocity will be two times faster than satellite B

B: The two satellites have the same speed

C: Satellite B's velocity will be two times larger than Satellite A

D: We need to know the orbital radius in order to compare the speeds of the satellites
I need help with understanding this problem. I had initially chosen B, that the two satellites had the same speed because the mass does not effect the velocities of each of the satellites considering they are in orbit. But that answer was marked incorrect by my instructor. What other answer could it be and why was I wrong?

What will be the orbits of the two masses relative to each other?

phinds said:
What will be the orbits of the two masses relative to each other?
As per the information given in the problem the orbits will be of the same speed in the same circular orbital path?

momoneedsphysicshelp said:
Homework Statement:: Two satellites are in the same circular orbit around the Earth. Satellite A has mass of m and satellite B mass of 2m. Which one of the following statements is true about the speeds of these satellites?
Relevant Equations:: A: satellite A's velocity will be two times faster than satellite B

B: The two satellites have the same speed

C: Satellite B's velocity will be two times larger than Satellite A

D: We need to know the orbital radius in order to compare the speeds of the satellites

I need help with understanding this problem. I had initially chosen B, that the two satellites had the same speed because the mass does not effect the velocities of each of the satellites considering they are in orbit. But that answer was marked incorrect by my instructor. What other answer could it be and why was I wrong?

momoneedsphysicshelp, Delta2 and phinds

If ##g## is the gravitational acceleration at the altitude of the common orbit, then $$g=\frac{V_A^2}{R_A}=\frac{V_B^2}{R_B}$$ and since ##R_A=R_B## (same orbit) it follows that $$V_A=V_B$$.

Orodruin and momoneedsphysicshelp
Thank you all, I will converse with my instructor regarding my reasoning.

Answer D is a true statement. But, the question specifies that the orbital radii are the same.

PeroK said:
Answer D is a true statement. But, the question specifies that the orbital radii are the same.
I do not read D that way. Since it is specified in the problem that the radii are the same, I read it as claiming that you need to know what the common radius is, which is wrong.

B is definitely correct and an instructor that marks it wrong even after this is pointed out should not be a physics instructor. The argument is very simple and already given in #5.

Delta2 and PeroK

## 1. What is universal gravitation?

Universal gravitation is a fundamental force of nature that describes the attraction between any two objects with mass. It is responsible for keeping planets in orbit around the sun, and for the formation of galaxies.

## 2. Who discovered universal gravitation?

Isaac Newton is credited with discovering universal gravitation in the late 17th century. He developed the law of universal gravitation, which states that every object in the universe attracts every other object with a force that is directly proportional to their masses and inversely proportional to the square of the distance between them.

## 3. How does universal gravitation affect the motion of objects?

Universal gravitation affects the motion of objects by exerting a force on them. This force, known as the gravitational force, causes objects to accelerate towards each other. The strength of the force depends on the masses of the objects and the distance between them.

## 4. What is the difference between mass and weight in relation to universal gravitation?

Mass is a measure of the amount of matter in an object, while weight is a measure of the force of gravity acting on an object. In relation to universal gravitation, the mass of an object determines the strength of the gravitational force it exerts on other objects, while weight is the result of the gravitational force acting on an object.

## 5. How does the distance between two objects affect the strength of their gravitational attraction?

The strength of the gravitational attraction between two objects is inversely proportional to the square of the distance between them. This means that as the distance between two objects increases, the gravitational force between them decreases. This is why objects on Earth experience less gravitational force from the sun than the Earth does, even though the sun has a much larger mass.

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