Understanding Velocity Calculation in Orbit: Exploring the Laws of Gravitation

In summary, the conversation discusses a problem involving a rocket orbiting the Earth and the calculation of its velocity and force. The speaker is confused about the discrepancy between their calculated velocity of 5609m/s and the answer key's velocity of 3950m/s. They also question the calculation of the velocity in relation to the center of mass it is orbiting around. The correct force is determined to be F=12268.1N.
  • #1
JM2107
In the following problem, I got that the velocity is 5609m/s but the answer key says that the velocity of the rocket is 3950m/s. I know both answers can be calculated but I don't understand why the radial distance would be the distance from the rocket to the Earth's surface. I personally think that the velocity of the rocket should be calculated in respect to the center of the mass that is is orbiting around. Could some please tell me if I am right, it would be greatly appreciated. Oh yeah, and I got the correct force which is F=12268.1N. Once again, thanks for any help provided in advance


Here's part of the problem:

1. A 5000 kg rocket orbits the Earth at an altitude above the earth’s surface equal to the radius of the earth[R_earth=6.4*10^6m].
a. Calculate the force exerted on the rocket by the earth.
b. Calculate:
i. the velocity of the rocket
 
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  • #2
Did you try to equate needed for orbiting centripetal acceleration v2/r to the acceleration of gravity g/4 at that distance? It comes right, v~4 km/sec
 

1. How is velocity calculated in orbit?

The velocity of an object in orbit is determined by the combination of its distance from the center of the object it is orbiting and the strength of the gravitational force acting on it. This can be calculated using the formula v = √(GM/r), where G is the gravitational constant, M is the mass of the central object, and r is the distance between the two objects.

2. What are the laws of gravitation?

The laws of gravitation, also known as Newton's laws of motion, describe the relationship between objects and the force of gravity acting between them. The three laws state that: 1) every object in the universe attracts every other object with a force directly proportional to their masses and inversely proportional to the square of the distance between them, 2) the force of gravity between two objects is equal in magnitude and opposite in direction, and 3) the force of gravity acting on an object is directly proportional to its mass and the acceleration due to gravity.

3. How does gravity affect an object in orbit?

Gravity is what keeps an object in orbit around another object. The gravitational force between the two objects causes the orbiting object to constantly accelerate towards the central object, but because of its tangential velocity, it continues to move forward and never falls into the central object. The combination of these two forces results in a circular or elliptical orbit.

4. What factors can affect an object's velocity in orbit?

The velocity of an object in orbit can be affected by several factors, including the mass of the central object, the distance between the two objects, and the shape and size of the orbit. Changes in any of these factors can alter the strength of the gravitational force and therefore impact the object's velocity in orbit.

5. Can the velocity of an object in orbit change?

Yes, the velocity of an object in orbit can change due to various factors such as gravitational forces from other objects, atmospheric drag, or propulsion from thrusters. In some cases, a change in velocity can result in the object falling out of orbit and either crashing into the central object or being flung out into space.

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