Centripetal acceleration of objects in orbit around the Earth

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Discussion Overview

The discussion revolves around the centripetal acceleration of satellites in orbit around the Earth, exploring the relationship between gravitational acceleration and tangential velocity. Participants examine the implications of these forces on the satellite's motion, particularly in the context of circular and elliptical orbits.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant notes that the gravitational acceleration for an orbiting satellite can range from 8.5 to 9.5 m/s² and questions how this relates to the satellite's constant tangential velocity while it accelerates downward.
  • Another participant clarifies that "downwards" is not a fixed direction in orbit, as it changes with the satellite's position along its orbital path, affecting how acceleration is perceived.
  • A participant suggests that the centripetal force experienced by the satellite results in a balance of radial accelerations, leading to no net change in radius or speed during circular motion.
  • It is mentioned that in elliptical orbits, gravitational effects can alter tangential speed at different points in the orbit, except at perigee and apogee.
  • One participant raises the possibility of energy loss due to air resistance at orbital heights, suggesting that this could lead to orbital decay.

Areas of Agreement / Disagreement

Participants express differing views on the nature of gravitational acceleration and its effects on orbital motion, with some agreeing on the balance of radial accelerations while others seek alternative explanations. The discussion remains unresolved regarding the best way to conceptualize these dynamics.

Contextual Notes

The discussion does not resolve the complexities of gravitational effects in different orbital shapes, nor does it clarify the assumptions about air resistance at orbital heights.

Love2teachPhys
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Hi all. The answer to this might be trivial. If it is, sorry for posting. If you calculate the acceleration due to gravity of an orbiting satellite, it could be around 8.5-9.5m.s-2, depending. So, it's tangential velocity is such that as it falls towards earth, Earth curves away and the satellite never comes closer to Earth - here's my problem. If it's is accelerating towards Earth at say 9m.s-2, then every second it's downward velocity increases by 9m.s-1. If it continually accelerates in this way, eventually you have massive downward velocity, yet tangential velocity remains constant...the satellite should come crashing down. So, perhaps it's reached terminal downward velocity? But there's scant air resistance.. what gives?
 
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"downwards" is not a fixed direction. As the satellite moves along its orbital path, "downwards" now is different from "downwards" a moment ago and from "downwards" a moment from now. After 1/4 of a complete orbit, the new "downwards" acceleration is no longer adding velocity along the original direction at all.
 
Love2teachPhys said:
Hi all. The answer to this might be trivial. If it is, sorry for posting. If you calculate the acceleration due to gravity of an orbiting satellite, it could be around 8.5-9.5m.s-2, depending. So, it's tangential velocity is such that as it falls towards earth, Earth curves away and the satellite never comes closer to Earth - here's my problem. If it's is accelerating towards Earth at say 9m.s-2, then every second it's downward velocity increases by 9m.s-1. If it continually accelerates in this way, eventually you have massive downward velocity, yet tangential velocity remains constant...the satellite should come crashing down. So, perhaps it's reached terminal downward velocity? But there's scant air resistance.. what gives?

OK You realize it doesn't actually get any closer so there has to be an explanation. Try this:
If you realize that every time the satellite goes round once, the centripetal force has pointed in all possible radial directions, each instant of acceleration in one direction is balanced out by an instant, radially opposite acceleration, when it gets round there. So the net effect will be zero change in radius (or speed). As jbriggs has already pointed out, "downwards" really means radial.
The above only applies in the case of circular motion. If the orbit is elliptical (most / all are like this) the effect of g at any point will be to add to or subtract from the tangential speed (except at perigee and apogee, of course).

If there is any significant quantity of air at the orbital height, energy is continually lost through friction so the orbit will decay, catastrophically.
 
Hmm. Thanks for the quick replies. I like the explanation that the net radial acceleration is zero, as for every radial acceleration, there is an opposite equal in magnitude acceleration. Is there another way of explaining this, perhaps?
 

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