Gravitational Satellite Angst

In summary: In this case v is the speed you calculated in A, m is the mass of the satellite, and r is the radius of the orbit (height + radius of Earth). In summary, we discussed the speed and period of a satellite in a circular orbit 640 km above the Earth's surface, which were calculated to be 7555.8 m/s and 5829.3 seconds, respectively. The total energy of the satellite in its orbit was found to be 6279885877 J, and the angular momentum about the centre of the Earth was calculated to be I (7555.8/7010000). To determine the satellite's altitude and speed after its 1500th revolution, we can use conservation of
  • #1
latitude
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A 220 kg satellite is in an approximatel circular orbit 640 km above the Earths surface.
a) Speed of satellite and the period of its orbit?
Vt^2 = GM/R
= (6.67 x 10^-11)(6 x 10^24) / (6.37 x 10^6 + 640000) (That's radius of Earth plus height of satellite)
= 7555.8 m/s
T^2 = (4pi^2 / GM) x R^3
= 4pi^2/ (6.67 x 10^-11)(6 x 10^24) x (7010000)^3 (again, radius of Earth plus heigh of satellite)
= 5829.3

b) Total energy of satellite in its orbit?
E = -1/2 (GMm/R)
= -1/2 (6.67 x 10^-11)(6 x 10^24)(220) / 7010000)
= 6279885877 J

c) What is the angular momentum of the satellite about the centre of the Earth?
L = Iw
L = I (vt/R)
= I (7555.8/7010000)


I'm stuck now. I am pretty sure my first few answers are wrong anyway. I don't have much grasp of the concepts of this fancy gravitational stuff, I don't think. The question goes on...

d) If the satellite loses 1.5 x 10^5 J per orbital revolution due to air resistance, determine the satellite's altitude and speed after its 1500th revolution.

e) What is the angular momentum of the satellite about the centre of the Earth after the 1500th revolution? Has angular momentum about the centre of the Earth been conserved? If not, explain what has caused the change.

Needless to say, I have no idea how to tackle these.
 
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  • #2
a, First start with Keplers law (T/2pi)^2 = r^3 / GM
Well done for spotting that r is the height + radius of Earth!
The speed is simple form the circumference of the orbit and period.

b, Remember total energy is kinetic + potential.

d, Use conservation of energy.
 
  • #3
A is ok. the second answer needs a unit.
for B you need the kinetic energy as well, and the equation you use for the potential energy has E = 0 as R goes to infinity, E <0 everywhere else. you probably want to have E=0 at the surface of the earth.
C angular momentum is m(v x R) (cross product of vectors) for circular motion it's simply
mvr
 

Related to Gravitational Satellite Angst

1. What is a gravitational satellite angst?

A gravitational satellite angst is a theoretical concept that describes the anxiety and uncertainty surrounding the use and impact of artificial satellites in orbit around Earth. It refers to the potential dangers and negative consequences that could arise from the increasing number of satellites being launched into space and their potential to disrupt the Earth's delicate gravitational balance.

2. How do gravitational satellites affect Earth's gravitational pull?

Gravitational satellites, also known as artificial satellites, have a negligible effect on Earth's overall gravitational pull. This is because the mass of these satellites is significantly smaller compared to the mass of the Earth. However, their constant presence in orbit can slightly disturb the Earth's gravitational field, leading to minor changes in the Earth's rotation and orbit.

3. Are there any potential risks associated with gravitational satellites?

Yes, there are potential risks associated with gravitational satellites, although they are currently only theoretical. These risks include collisions between satellites, which could create space debris and potentially damage other satellites or spacecraft. Additionally, the increasing number of satellites in orbit could also lead to overcrowding and interference with satellite communication and navigation systems.

4. How are scientists addressing the concerns surrounding gravitational satellite angst?

Scientists and space agencies are actively working to address the concerns surrounding gravitational satellite angst. This includes implementing strict regulations for satellite launches and developing technology to safely remove defunct satellites from orbit. Additionally, research is being conducted to better understand the effects of satellites on the Earth's gravitational field and how to mitigate any potential risks.

5. Can gravitational satellites be used for positive purposes?

Yes, gravitational satellites have many positive uses, including communication, navigation, weather monitoring, and scientific research. They also play a crucial role in space exploration and studying the Earth's climate and environment. However, it is important to carefully consider and address any potential risks associated with their use to ensure that they do not have a negative impact on our planet.

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