# Cost of setting up a sattelite?

• Zaros
In summary, the conversation discusses the amount of work needed to put an experimental package into orbit around the Earth and how it relates to the extra energy required for deployment. The equation W=F*d is used to calculate the work, but it is not applicable in this scenario. The relationship between work and energy is explored, with the correct equation being W = KE + PE = 1/2 mv^2 + mgh. However, this equation assumes a uniform gravity field and the conversation prompts the use of the equation F=(G*m1*m2)/r^2 to account for the changing force of gravity. The conversation concludes with a reminder to think carefully about the problem and consider the change in potential energy of the package.
Zaros

## Homework Statement

A scientist wants to put an 100kg experimental package in orbit around the Earth. The cost of deployment depends on the amount of extra energy it takes to get it into the required position i.e. how much more energy is used than just sending the rocket up there.
a) Determine the amount of work that must be done to get the package to 1 000km above the Earth’s surface.
b) Determine the amount of extra work needed to put the package into a circular orbit at this height.

W=F*d
F=(G*m1m2)/r2

## The Attempt at a Solution

a) W=F*d
F=FG
=(Gm1m2)r2
=(6.67 * 10-11 * 100 * ME)/(RE + 1000000)2
= 731 N
W= F*d = 730 * 1000000
= 7.31 *108

Zaros said:
W=F*d
That is true only for a constant force.

You need to use something else. Hint: What is the relation between work and energy?

Work is equal to kinetic energy i.e. W= 1/2 mv2
Is that what your getting at?

What about potential energy?

W = KE + PE = 1/2 mv2 + mgh
Is that right?

No. That mgh term is assuming a uniform gravity field.

then should i use the F= (G*m1*m2)/r2 instead so that would lead to
F= 1/2 mv2 + h((G*m1*m2)/r2)

Now is this correct?

Zaros said:
then should i use the F= (G*m1*m2)/r2 instead so that would lead to
F= 1/2 mv2 + h((G*m1*m2)/r2)

Now is this correct?

Stop just throwing equations at the problem. You equated F, Force, with an energy. Not good. You need to stop and think about the problem.

What would your change in potential energy be if you were to take the package on the ground with 0 kinetic energy and put it up into space at the height required and still not let it have any kinetic energy?

## 1. What is the average cost of setting up a satellite?

The average cost of setting up a satellite can vary greatly depending on the type and purpose of the satellite. However, on average, it can range from $50 million to$400 million.

## 2. What factors contribute to the cost of setting up a satellite?

Several factors contribute to the cost of setting up a satellite, including the design and construction of the satellite itself, launch vehicle and launch services, ground support equipment, insurance, and operational costs.

## 3. How long does it take to set up a satellite?

The timeline for setting up a satellite can vary depending on the complexity and purpose of the satellite. Generally, it can take anywhere from 1 to 3 years to design, build, and test a satellite before it is ready for launch.

## 4. Are there any ongoing costs associated with maintaining a satellite?

Yes, there are ongoing costs associated with maintaining a satellite, including ground station operations, tracking and data collection, and satellite control and maintenance. These costs can vary depending on the type and purpose of the satellite.

## 5. Can the cost of setting up a satellite be recovered?

In most cases, the cost of setting up a satellite cannot be fully recovered. However, depending on the purpose of the satellite, it may generate revenue through services, such as telecommunications or remote sensing, which can help offset the initial cost.

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