Universal Gravitation - Satellites

In summary, the Explorer VIII satellite, launched in 1960, was designed to study the ionosphere and had an orbit with a perigee of 459 km and an apogee of 2289 km. The ratio of the speed at perigee to that at apogee can be found by using conservation of angular momentum and adding the Earth's radius to each distance. The resulting ratio is approximately 4.99 km.
  • #1
BbyBlue24
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0
The Explorer VIII satellite, placed into orbit November 3, 1960, to investigate the ionosphere, had the following orbit parameters: perigee, 459 km; apogee, 2289 km (both distances above the Earth's surface); period, 112.7 min. Find the ratio vp/va of the speed at perigee to that at apogee.
 
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  • #2
Welcome to Physicsforums, BbyBlue.

First off, questions like this should be submitted to the homework help section.

Second, before you can expect an answer, you should at least post what you have tried to get an answer.

It doesn't benefit you to have someone do your homework for you.
 
  • #3
FYI: This isn't a homework problem, I am doing random problems throughout the book to prepare for an exam tomorrow.

I have played around with equations of conservation of angular momentum and equations such as v=(2πr)/T and v=√(GMe/r)=√(GMe/Re+h). I tried using Vp=(Ra/Rp)Va, but I have gotten nowhere. Thanks!
 
  • #4
Well, by using conservation of angular momentum for the satellite

[tex] r_{perigee} v_{perigee} = r_{apogee} v_{apogee} [/tex]

we rearrange this to:

[tex] \frac{v_{perigee}}{v_{apogee}} = \frac{r_{apogee}}{r_{perigee}} [/tex]

you don't need the period.
 
  • #5
I have; Vp/Va = Ra/Rp = 2289/459 = 4.99 km
 
  • #6
The problem states distances above the surface, you need to add the Earth radius to each of those radius.
 
  • #7
I got it, thanks! I think that's all I have tonight, thank you very much!
 
  • #8
good luck on your test.
 

1. What is Universal Gravitation and how does it relate to satellites?

Universal Gravitation is the scientific law that explains the force of attraction between all objects with mass. It relates to satellites because it is the force that keeps them in orbit around larger objects, such as planets or moons.

2. How do satellites stay in orbit without falling back to Earth?

Satellites stay in orbit because of the balance between their forward motion and the gravitational pull of the larger object they are orbiting. This results in a circular or elliptical path around the object, rather than falling back to Earth.

3. Can satellites have different orbits around the same planet?

Yes, satellites can have different orbits around the same planet. Their orbits depend on factors such as their altitude, speed, and direction of travel, which can be adjusted to achieve a desired orbit for different purposes.

4. How does the mass of a satellite affect its orbit?

The mass of a satellite does not affect its orbit around a larger object. The force of gravity between two objects depends on their masses, but in the case of satellites, the mass of the smaller object is negligible compared to the larger object, so it does not significantly impact the orbit.

5. Can satellites orbit any other object besides planets?

Yes, satellites can orbit any object with enough mass and gravitational pull, such as moons, asteroids, or even other satellites. However, the orbit may be different depending on the size and mass of the object being orbited.

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