Satellite Orbit Around Mars: Force & Speed Calculation

In summary, scientists are planning to place a 2500 kg satellite in orbit around Mars at a distance equal to 1.8 times the radius of Mars above the surface of the planet. Using the given information of mmars = 6.4191 x 1023 kg, rmars = 3.397 x 106 m, and G = 6.67428 x 10-11 N-m2/kg2, the force of attraction between Mars and the satellite was calculated to be 2864.722760095893N. However, it was found that the distance between the centers of mass of the two objects needed to be used, which is 2*1.8 rmars. The formula for this
  • #1
mrshappy0
99
0
Scientists want to place a 2500 kg satellite in orbit around Mars. They plan to have the satellite orbit a distance equal to 1.8 times the radius of Mars above the surface of the planet. Here is some information that will help solve this problem:

mmars = 6.4191 x 1023 kg
rmars = 3.397 x 106 m
G = 6.67428 x 10-11 N-m2/kg2

1)What is the force of attraction between Mars and the satellite?
I got 2864.722760095893N but the online HW program says I am wrong and that I need to add one more radius. This is the formula I used: (2500(6.674282(10^-11))(6.4191(10^23)))/(1.8(3.397(10^6)))^2

2)What speed should the satellite have to be in a perfectly circular orbit?

No idea where to start with this one. Should I start with a free body diagram. I think I would have the W vector pointing in towards the center of Mars and I would have to make the movement along the vertical axis (y) 0 and the movement along the horizontal axis (x) constant. Correct?
 
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  • #2
This isn't a HW problem. I am just studying. I have spent a fair amount of time on this and can't get it right.
 
  • #3
mrshappy0 said:
Scientists want to place a 2500 kg satellite in orbit around Mars. They plan to have the satellite orbit a distance equal to 1.8 times the radius of Mars above the surface of the planet. Here is some information that will help solve this problem:

mmars = 6.4191 x 1023 kg
rmars = 3.397 x 106 m
G = 6.67428 x 10-11 N-m2/kg2

1)What is the force of attraction between Mars and the satellite?
I got 2864.722760095893N but the online HW program says I am wrong and that I need to add one more radius. This is the formula I used: (2500(6.674282(10^-11))(6.4191(10^23)))/(1.8(3.397(10^6)))^2

2)What speed should the satellite have to be in a perfectly circular orbit?

No idea where to start with this one. Should I start with a free body diagram. I think I would have the W vector pointing in towards the center of Mars and I would have to make the movement along the vertical axis (y) 0 and the movement along the horizontal axis (x) constant. Correct?

Welcome to the PF.

You are correct to post here in the HH forums -- all schoolwork-type problems should be posted here. And it is good that you are showing your work.

The questions uses the words "above the surface of the planet", so that's why you need to add in one radius of the planet to get your attractive force calculation based on the distance between the centers of mass of the two objects.

And for the orbital speed, are you familiar with the equation(s) for uniform circular motion due to an attractive force?
 
  • #4
Q1: I plugged in a 2 for another radius and got this: (2500(6.674282(10^-11))(6.4191(10^23)))/(1.8(2(3.397(10^6))))^2 = 716.1806900239733. The answer seems to be incorrect again. puzzled. I must be reading something wrong.

Q2: Uniform circular motion- so use centripetal acceleration (a=(v^2)/Radius)?
 
  • #5
mrshappy0 said:
Q1: I plugged in a 2 for another radius and got this: (2500(6.674282(10^-11))(6.4191(10^23)))/(1.8(2(3.397(10^6))))^2 = 716.1806900239733. The answer seems to be incorrect again. puzzled. I must be reading something wrong.

Q2: Uniform circular motion- so use centripetal acceleration (a=(v^2)/Radius)?

Q1: The satellite will be 1.8 times the radius of Mars *above* Mars. So the total distance is not 2*1.8 rmars... What is it?

(And there is no reason to show more than 3-4 digits past the decimal point in your answers.)

Q2: Correct! Keep on going!
 
  • #6
Q1: simple. Thanks.

Q2: Wow physics just baffles me. It's like magic. Lately it is just clicking for me and it never has until today. Knock on wood-I know it gets harder but it is a start. Thanks for your time.
 
  • #7
mrshappy0 said:
Q1: simple. Thanks.

Q2: Wow physics just baffles me. It's like magic. Lately it is just clicking for me and it never has until today. Knock on wood-I know it gets harder but it is a start. Thanks for your time.

Glad that it's starting to click, and glad to help. :smile:
 

1. How does the force of gravity affect the orbit of satellites around Mars?

The force of gravity is the main factor that determines the orbit of satellites around Mars. The larger the mass of the planet, the greater the force of gravity, and the faster the satellite will need to orbit to maintain its position. Therefore, the force of gravity plays a crucial role in calculating the speed and trajectory of satellites around Mars.

2. What is the speed of a satellite in orbit around Mars?

The speed of a satellite in orbit around Mars depends on its altitude, or distance from the surface of the planet. The closer the satellite is to Mars, the faster it will need to orbit to maintain its position. On average, satellites in low Mars orbit have a speed of around 3.5 kilometers per second, while those in higher orbit can have speeds of up to 5 kilometers per second.

3. How do scientists calculate the force and speed of a satellite's orbit around Mars?

To calculate the force and speed of a satellite's orbit around Mars, scientists use a combination of mathematical equations and data from the satellite's position and velocity. These calculations take into account the mass of the planet, the distance between the satellite and Mars, and the gravitational constant. By plugging these values into the appropriate equations, scientists can determine the force and speed of the satellite's orbit.

4. Can the orbit of a satellite around Mars change over time?

Yes, the orbit of a satellite around Mars can change over time due to various factors such as atmospheric drag, gravitational pull from other objects, and the changing shape of the planet's surface. Scientists continuously monitor and make adjustments to the orbits of satellites to ensure they remain in the desired position and avoid any potential collisions.

5. How does the orbit of a satellite around Mars affect its ability to gather data?

The orbit of a satellite around Mars can greatly impact its ability to gather data. A satellite in a higher orbit will have a wider field of view and can cover more area, making it better for mapping and surveying missions. On the other hand, a satellite in a lower orbit can gather more detailed data but will have a smaller coverage area. The orbit of a satellite is carefully chosen based on the objectives of the mission and the type of data that needs to be collected.

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