# Time it takes for a satellite to orbit the Earth

• balletgirl
In summary, we determined the time it takes for a satellite to orbit the Earth in a circular "near-Earth" orbit by setting the acceleration due to gravity equal to the centripetal acceleration of the satellite. We used the equation g= GM/r^2 and plugged in the values for the mass of the Earth, radius of the Earth, and the gravitational constant. After solving for the velocity of the satellite, we used this value to find the period using the equation T= 2πr/v. The result does not depend on the mass of the satellite.

## Homework Statement

Determine the time it takes for a satellite to orbit the Earth in a circular "near-Earth" orbit. The definition of "near-Earth" orbit is one which is at a height above the surface of the Earth which is small compared to the radius of the Earth, so that you may take the acceleration due to gravity as essentially the same as that on the surface. Does your result depend on the mass of the satellite?

M(earth)= 5.98x10^24 kg
R(earth)=6.38x10^6 m
G= 6.67x10^-11

g= GM/r^2

FG= Gm1m2/r^2

## The Attempt at a Solution

I am not sure where to start since I don't know what equation to use.

One more equation might help you. The satellite in orbit will have an acceleration equal to $$a = \frac{v^2}{r}$$ which will equal Earth's gravity, $$g = \frac{GM}{r^2}$$

Setting those equal to each other, can you determine the velocity of the satellite and use that to find the period?

The gravitational force between the Earth and the satellite provides the centripetal force of the satellite. Are you able to make an equation?

Okay, I'm not sure if this is right, but here's my attempt:

I did v^2/r = GM/r^2
& plugged in:
V^2/(6.38x10^6) = (6.67x10^-11)(5.98x10^24)/(6.38x10^6)

and ended up with:
V= 1.99x10^7 m/s

when i plugged it into a=v^2/r i got a= 6.25x10^7

this doesn't seem right, isn't is suppose to be near 9.8 m/s?

You didn't square the radius on the right side.

Wow, dumb mistake...I redid it by squaring it and got 9.796 m/s. Thank you for your help!

## 1. How long does it take for a satellite to orbit the Earth?

The time it takes for a satellite to orbit the Earth depends on its altitude and the type of orbit it is in. On average, a satellite in a low Earth orbit (LEO) takes about 90 minutes to complete one orbit, while a geostationary satellite takes 24 hours.

## 2. What affects the time it takes for a satellite to orbit the Earth?

The main factors that affect the time it takes for a satellite to orbit the Earth are the altitude of the satellite and the mass of the Earth. The lower the altitude, the faster the satellite will orbit due to less gravitational pull. Similarly, a heavier Earth will result in a longer orbital time.

## 3. Can the time it takes for a satellite to orbit the Earth vary?

Yes, the time it takes for a satellite to orbit the Earth can vary due to changes in its altitude, orbital speed, and gravitational forces. For example, a satellite may experience orbital decay and its time to orbit may decrease as it moves closer to Earth's atmosphere.

## 4. How does the time it takes for a satellite to orbit the Earth affect its communication capabilities?

The time it takes for a satellite to orbit the Earth can affect its communication capabilities as it determines the amount of time the satellite is in range of a ground station. A satellite in a lower orbit will have a shorter communication window compared to one in a higher orbit.

## 5. Can the time it takes for a satellite to orbit the Earth be changed?

Yes, the time it takes for a satellite to orbit the Earth can be changed by altering its altitude or orbital speed. This can be done through thruster burns or gravitational assistance from other objects in space. However, these changes must be carefully planned and executed to maintain the satellite's intended orbit.