Determine the value that has the largest total energy. Assuming that the orbirts are circular.
(a) 1000 kg satellite at geosynchronous orbit
(b) 1000 kg satellite in low earth orbit—roughly 300 km
(c) 500 kg satellite at geosynchronous orbit
(d) A 500 kg satellite in low earth orbit—roughly 300 km
(e) not given enough information
I say c,am i right?
Correct. You can easily calculate this. You can also see this as follows. All the energies are negative, so the object with the largest energy is that object which requires the least energy to escape to infinity.
To determine which value has the largest total energy, we need to consider the formula for the total energy of an orbiting satellite, which includes both its kinetic energy and potential energy. The formula is:
Total Energy = Kinetic Energy + Potential Energy
For circular orbits, the formulas for the kinetic energy and potential energy are given by:
Kinetic Energy = (1/2) * m * v^2
Potential Energy = G * (m * M) / r
where:
m = mass of the satellite
v = velocity of the satellite
G = gravitational constant
M = mass of the Earth
r = radius of the orbit
We can simplify the comparison by noting that the mass of the satellites is the same (1000 kg or 500 kg). Therefore, we can disregard the mass when comparing the total energy values.
Geosynchronous Orbit: In a geosynchronous orbit, the satellite's period (time taken to complete one orbit) matches the Earth's rotational period, which is roughly 24 hours. This means that the satellite is positioned at a very high altitude, which makes the radius of the orbit larger compared to low Earth orbits.
Low Earth Orbit: In a low Earth orbit, the satellite is positioned much closer to the Earth's surface and has a shorter orbital period, typically around 90 minutes. This results in a smaller radius for the orbit.
Comparing (a) and (c):
Since the radius of the orbit is larger for the geosynchronous orbit, the potential energy will be larger. Therefore, (c) will have a larger total energy compared to (a).
Comparing (b) and (d):
These two cases have the same radius since they are both in low Earth orbit. Therefore, we need to compare the velocities to determine which one has a larger total energy. Given that the mass is the same, the satellite with a higher velocity will have a larger total energy. Thus, (b) will have a larger total energy compared to (d).
Based on this analysis, the satellite with the largest total energy is option (c) - the 500 kg satellite at geosynchronous orbit. So your answer is correct.