Does Mass Affect the Orbital Velocity of Satellites?

AI Thread Summary
The discussion focuses on the relationship between mass and orbital velocity for satellites in circular orbits around Earth. It establishes that the orbital velocity is derived from the gravitational force acting on the satellite, where the formula v = √(Gm/r) applies. When a second satellite with mass three times that of the first is introduced, it is shown that its orbital velocity remains the same, as mass cancels out in the gravitational equation. The key takeaway is that orbital velocity is independent of the satellite's mass, relying solely on the radius of the orbit and the gravitational constant. This conclusion is supported by mathematical reasoning based on Newton's laws of motion and gravitational force.
scientict
Messages
3
Reaction score
0

Homework Statement



A science group put in a satellite of mass m kg into a circular Earth orbit of radius r. The orbital velocity it needs to remain in this orbit is v. They now put another satellite into a similar orbit at the same altitude. Its mass is 3 times m. What orbital velocity would it need to be given? Give reasons using mathematical reasoning.

Homework Equations



Newton's law v = 2pi x r/T

The Attempt at a Solution



v^2/r=G m/r^2
Satellite 1:
v=√(G m/r)
Satellite 2:
v=√(G 3m/r)
 
Physics news on Phys.org
scientict said:

The Attempt at a Solution



v^2/r=G m/r^2

What does 'm' represent here? Can you derive this formula?

When a body moves with constant v in a circular orbit, the centripetal force is constant and equal to the force due to Earth's gravity on the body. Now you can deduce the correct version of the above formula using this.
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Calculate Mass of Satellite: Step-by-Step Guide
Replies
16
Views
2K
What is the Correct Radius and Mass of Earth for Satellite Orbit Calculations?
Replies
1
Views
2K
Change in momentum for a satellite in circular orbit
Replies
6
Views
3K
Potential Energy and raising a satellite from Earth into a Circular Orbit
Replies
5
Views
2K
How Does Satellite Mass Impact Velocity Change for Circular Orbit Achievement?
Replies
5
Views
2K
Finding r of a Jovian-synchronous orbit and escape velocity
Replies
7
Views
2K
How much work is done when a satellite is launched into orbit?
Replies
5
Views
2K
A satellite in orbit in a system with one planet and two moons
Replies
1
Views
1K
Find the speed of a satellite at a distance R from Earth
Replies
39
Views
4K
Doubling speed in circular orbit to attain elliptical orbit
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top