# Satellite moving in a stable circular orbit

• ronartest
In summary: Note that you need to divide by km^2 (not just km) to get the units right.Once you have that, you have the units on the left side of your equation. What about the units on the right side of the equation? Well, what is the definition of acceleration? Do you know what the units on your answer should be?After that, you can use the equation a = v^2 / r to solve for v, remembering to include units in that equation as well and to make sure they all work out correctly (i.e. that you don't end up with units of meters on one side and kilometers on the other).In summary, to calculate the speed of a 600kg satellite
ronartest

## Homework Statement

A 600kg satellite moving in a stable circular orbit about the Earth at a height of 4000km (G=6.67x10^-11 NM^2/kg^2, Re=6380km, Me=5.98x10^24kg).
Calculate the speed of the satellite at that height.
Calculate the orbital period (T), the time for one revolution
Calculate the gravity at height h=4000 km.

## Homework Equations

Gravitational Force: F=Gm1m2/r^2
centripetal acceleration: a= v^2/r
Period (circular motion): T=2(pie)r/v

## The Attempt at a Solution

calculated a gravitational force of 2221179013, plugged it into F=ma, which I came out as 2221179013=600a. Got an acceleration of 3701965.021=v^2/r, which came out to v2= 3701965.02*10380. After taking the square root of that, I finished with v=196026.52m/s, which is off from the correct answer which is 6198.9 m/s. Where did I go wrong, how can I take the right steps? Thanks so much.

I've been working on this question for a couple hours now and I can't seem to get a different answer. Is it possible that the answer given in the study guide is incorrect?

I just need help for the velocity part. I have a final on this tomorrow, can someone please help me find the error in my calculation? Thanks.

Your calculation is pretty much meaningless to me because you don't have any units attached to your numbers. I can't tell what error you might have made unless you have the proper units on each value.

For what it's worth, I was easily able to confirm the answer in the study guide, about 6.2 km/s.

You nailed it diazona (well, almost. It would have helped if ronartest had shown some work.)

Units, ronartest! These quantities are not just numbers.

Yay! Finally someone who cares as much as I do about units ;-)

Haha, yeah I'm really sorry about that. To be honest, I'm not really sure of the units on anything except the initial numbers. That said for the gravitational force I multiplied NM^2/kg^2 by kg by kg divided by km, whatever that comes out to. I guess the acceleration would be m/s^2. Is it not possible to understand the steps I am taking? Would it be possible to explain the steps that you took to achieve your answer? Again, I'm sorry for not being more clear, and I greatly appreciate your interest.

Would you attempt to do this problem without knowing how to multiply? Because that's just what you did. You really can't expect to be able to solve physics problems without knowing how to do basic math, and that includes both numbers and units.

So what are the units on the gravitational force you calculated?
$$F = G\frac{m_1 m_2}{r^2}$$
You're right that G has units of N m^2/kg^2 (it's lowercase m for meters, not capital M), and both m1 and m2 have units of kilograms, and that r has units of kilometers (but note that r is squared in the denominator). How would you figure out the result of multiplying (N m^2/kg^2) * kg * kg / km^2?

## 1. What is a satellite in a stable circular orbit?

A satellite in a stable circular orbit is a man-made object that is launched into space and moves around the Earth in a circular path, maintaining a constant distance from the Earth's center. This orbit is considered stable because the satellite's speed and direction are balanced by the gravitational pull of the Earth, allowing it to continuously orbit without falling towards or drifting away from the planet.

## 2. How does a satellite maintain a stable circular orbit?

A satellite maintains a stable circular orbit by moving at a constant speed and direction, known as its orbital velocity. This velocity is determined by the mass of the satellite, the mass of the Earth, and the distance between them. The gravitational force between the two objects keeps the satellite in its orbit, while the centrifugal force, caused by the satellite's speed, balances it out, creating a stable circular motion.

## 3. What factors can affect the stability of a satellite's orbit?

The stability of a satellite's orbit can be affected by several factors, such as the mass and shape of the satellite, atmospheric drag, and the gravitational pull of other celestial bodies, such as the Moon or the Sun. Changes in these factors can alter the satellite's orbital velocity and direction, causing it to deviate from its stable orbit.

## 4. How long can a satellite remain in a stable circular orbit?

A satellite can remain in a stable circular orbit for an indefinite amount of time, as long as it is not affected by external forces or runs out of fuel. However, the orbit may gradually decay over time due to atmospheric drag, causing the satellite to eventually fall back to Earth or enter a different type of orbit.

## 5. How are satellites used in stable circular orbits?

Satellites in stable circular orbits are used for various purposes, such as communication, navigation, weather forecasting, and scientific research. They provide a stable platform for collecting and transmitting data, as well as monitoring different areas of the Earth's surface. Some satellites also play a crucial role in space exploration and surveillance activities.

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