• jj8890
In summary, the conversation was about a problem involving a geosynchronous satellite orbiting a planet at a given radius and its angular speed being the same as the Earth's rotational speed. The problem asked for the force acting on the satellite and the mass of the planet. The equations used to solve the problem were v= (2*pi*R)/T, v= (Sqrt(G * Mcentral))/R, and F=(GmM)/r^2. The correct solutions were found to be 1016.21 N for the force and 6.43615 * 10^26 kg for the mass of the planet.
jj8890

## Homework Statement

Given: G = 6.67259 × 10^-11 N m^2/kg^2 .
A 956 kg geosynchronous satellite orbits a planet similar to Earth at a radius 201000 km
from the planet’s center. Its angular speed at this radius is the same as the rotational speed of the Earth, and so they appear stationary in the sky. That is, the period of the satelliteis 24 h .

What is the force acting on this satellite? (Newtons)
What is the mass of this planet? (kgs)

I just need help checking my answers and make sure that I am using the correct equations. I would appreciate the help.

## Homework Equations

v= (2*pi*R)/T
v= (Sqrt(G * Mcentral))/R; G=6.67259 *10^-11
F=(GmM)/r^2

## The Attempt at a Solution

v= (2*pi*R)/T = (2*pi*201,000,000)/86400 = 14617.1 m/s

v= (Sqrt(G * Mcentral)); (v^2 *r)/G=Mcentral
Mcentral= (14617.1^2 * 201,000,000)/(6.67259 *10^-11)= 6.43615 * 10^26 kg

F=(GmM)/r^2
F= [(6.67259*10^-11) * (956) * (6.43615 *10^26)]/(86400^2)=5.49985 *10^9 N

Where did the 86400 come from in your force equation?

Your speed seems fine, and I would probably use $F=m\frac{v^2}{r}$ for the force due to circular motion, which gives 1.016 kN. The mass of the planet is then 643*10^24 kg, as you have.

The 86400 = 24 hrs in seconds, the period. I also thought that the force was high...I'll recalculate.

I also got 1016.21 N when recalculated...thanks

## 1. What is a circular orbit?

A circular orbit is a type of orbit in which an object revolves around another object at a constant distance, forming a perfect circle. This type of orbit is commonly seen in the solar system, with planets revolving around the sun in circular paths.

## 2. How is a circular orbit different from an elliptical orbit?

A circular orbit is a special case of an elliptical orbit, in which the eccentricity (measure of how circular or elongated the orbit is) is equal to 0. In an elliptical orbit, the eccentricity is greater than 0, resulting in a non-circular path.

## 3. What factors determine the shape of a circular orbit?

The shape of a circular orbit is determined by the mass of the objects involved, their distance apart, and the velocity of the orbiting object. These factors must be in balance for a circular orbit to be maintained.

## 4. Can objects in a circular orbit change their speed?

Yes, objects in a circular orbit can change their speed. This can be achieved through the application of external forces such as thrust or gravitational pulls from other objects. However, the change in speed must be done carefully to maintain the balance of forces and keep the orbit circular.

## 5. What are some real-life examples of objects in circular orbits?

The moon orbiting around the Earth, Earth orbiting around the sun, and satellites orbiting around the Earth are some common examples of objects in circular orbits. Artificial satellites, such as those used for communication and navigation, are also placed in circular orbits around the Earth.

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