The discussion revolves around determining the speed of a satellite at a distance R from Earth, with a focus on gravitational forces and orbital mechanics. Participants explore concepts related to gravitational force, orbital velocity, and mechanical energy in the context of circular orbits.
The discussion is ongoing, with various interpretations of the problem being explored. Some participants have offered guidance on the relationships between gravitational force, kinetic energy, and potential energy, while others are seeking clarification on the problem statement and the variables involved.
There is some ambiguity regarding the definition of R (whether it refers to the radius of Earth or the distance from the satellite to Earth's center), and participants are questioning the implications of these definitions on the calculations. Additionally, the discussion touches on the concept of mechanical energy being negative in bound orbits.
No. Do not mix g and G. You know that GM/R2=g, so GM=gR2.Helly123 said:So, the total mechanical energy
= Ek + Ep = 1/2mv^2 + (-GmM/r) = gRm/4 - GmM/2R = -mgR/2. Is it?
Yesehild said:No. Do not mix g and G. You know that GM/R2=g, so GM=gR2.
So what result did you get?Helly123 said:Yes
Helly123 said:So, r = 2R
r is distance from satellite to Earth's center
Btw, mechanical energy is Ek. The answer is -mGR/4
How can Ek be negative?
PeterO said:NO. The Mechanical Energy is the sum of the Gravitational Potential Energy plus the Kinetic Energy. The Kinetic Energy may be positive, but the Mechanical Energy value can still be negative, provided the Potential Energy is negative, and larger in size than the Kinetic Energy.
I seePeterO said:NO. The Mechanical Energy is the sum of the Gravitational Potential Energy plus the Kinetic Energy. The Kinetic Energy may be positive, but the Mechanical Energy value can still be negative, provided the Potential Energy is negative, and larger in size than the Kinetic Energy.
Yes.Helly123 said:Ok. My answer is like Ep + Ek
While the formula i know for Ep is -GMm/r
r = 2R
Ek as usual is 1/2mv^2
V = ##\sqrt{ gmR/2}##
Ep + Ek
-GMm/2R + mgR/4 = -mgR/2 + mgR/4 = -mgR/4
Is that it?
Okehild said:Yes.