Maximum distance in orbit from center of a planet

AI Thread Summary
The discussion focuses on calculating the initial speed (v0) required for a satellite to reach a maximum distance of 5R/3 from the center of a nonrotating planet. Participants reference the conservation of energy and angular momentum principles, noting the need to express the gravitational potential energy V(r) in terms of G, M, and R. The angular momentum is equated at the satellite's launch and its highest point in orbit. There is a mention of the gravitational acceleration formula a = GM/R^2, but its relevance is questioned. The conversation emphasizes the application of these physics concepts to solve the problem effectively.
gcfve
Messages
13
Reaction score
0

Homework Statement


Consider a spherical, nonrotating planet of mass M, and radius R, with no atmosphere. A satellite is fired from the surface of the planet with speed v0 at 45o from the local vertical. In its subsequent orbit the satellite reaches a maximum distance of 5R/3 from the centre of the planet. Use conservation of energy and angular momentum to find vo in terms of G, M, R.


Homework Equations



E=\frac{1}{2}mvr2+L2/2mr2+V(r)



The Attempt at a Solution


so far all I have is a=GM/R^2, which I probably don't even need.
 
Physics news on Phys.org
Have you got a formula for V(r)?
Also need to work on momentum:
Angular momentum at start = angular momentum at apogee
 
Well, L=mrv or L=mbv0
and i guess V=-GmM/r but i don't know how to use these at this point..
 

Thread 'Rolling without slipping on a curved surface'

Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
View full post »
Thread 'Voltmeter readings for this circuit with switches'

Thread 'Voltmeter readings for this circuit with switches'

TL;DR Summary: I would like to know the voltmeter readings on the two resistors separately in the picture in the following cases , When one of the keys is closed When both of them are opened (Knowing that the battery has negligible internal resistance) My thoughts for the first case , one of them must be 12 volt while the other is 0 The second case we'll I think both voltmeter readings should be 12 volt since they are both parallel to the battery and they involve the key within what the...
View full post »
Thread 'Trying to understand the logic behind adding vectors with an angle between them'

Thread 'Trying to understand the logic behind adding vectors with an angle between them'

My initial calculation was to subtract V1 from V2 to show that from the perspective of the second aircraft the first one is -300km/h. So i checked with ChatGPT and it said I cant just subtract them because I have an angle between them. So I dont understand the reasoning of it. Like why should a velocity be dependent on an angle? I was thinking about how it would look like if the planes where parallel to each other, and then how it look like if one is turning away and I dont see it. Since...
View full post »

Similar threads

Calculating Angle & Speed to Reach Planet's Moon from Station Orbit
Replies
1
Views
2K
A satellite in orbit in a system with one planet and two moons
Replies
1
Views
1K
From circular orbit to elliptical orbit
Replies
3
Views
2K
Orbital speed variation as a planet orbits the Sun
Replies
5
Views
2K
Finding Orbital Period of Unknown Planet
Replies
5
Views
2K
How to find the acceleration due to gravity inside a planet?
Replies
3
Views
5K
Finding r of a Jovian-synchronous orbit and escape velocity
Replies
7
Views
2K
Doubling speed in circular orbit to attain elliptical orbit
Replies
3
Views
2K
Calculate the mass of a star and a planet that orbits it
Replies
12
Views
3K
Satellite Motion Homework: Find 2nd Satellite Speed
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top