Maximum distance in orbit from center of a planet

In summary, the conversation discusses the use of conservation of energy and angular momentum to find the initial speed of a satellite fired from a nonrotating planet with no atmosphere. The given parameters are the mass and radius of the planet, as well as the maximum distance the satellite reaches in its orbit. The equations used include the formula for gravitational potential energy, the formula for angular momentum, and the formula for velocity. The conversation ends with the clarification that the formula for velocity is needed in order to solve the problem.
  • #1
gcfve
13
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=[tex]\frac{1}{2}[/tex]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.
 
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  • #2
Have you got a formula for V(r)?
Also need to work on momentum:
Angular momentum at start = angular momentum at apogee
 
  • #3
Well, L=mrv or L=mbv0
and i guess V=-GmM/r but i don't know how to use these at this point..
 

FAQ: Maximum distance in orbit from center of a planet

What is meant by "maximum distance in orbit from center of a planet"?

The maximum distance in orbit from center of a planet refers to the farthest point in an orbit around a planet where an object or satellite is at its greatest distance from the planet's center.

How is the maximum distance in orbit from center of a planet calculated?

The maximum distance in orbit from center of a planet is calculated using Kepler's third law, which states that the square of the orbital period of an object is proportional to the cube of the semi-major axis of its orbit. Using this law, the maximum distance can be calculated by knowing the orbital period and the mass of the planet.

Can the maximum distance in orbit from center of a planet vary?

Yes, the maximum distance in orbit from center of a planet can vary depending on the shape and size of the planet's orbit. For example, in an elliptical orbit, the distance will vary as the object moves closer or farther away from the planet's center.

What factors can affect the maximum distance in orbit from center of a planet?

The maximum distance in orbit from center of a planet can be affected by the mass and size of the planet, as well as the shape of its orbit. Other factors such as gravitational pull from other objects and atmospheric drag can also have an impact on the maximum distance.

Why is it important to know the maximum distance in orbit from center of a planet?

Knowing the maximum distance in orbit from center of a planet is important for space missions and satellite operations. It helps in determining the stability and feasibility of an orbit, as well as predicting any potential hazards or risks that may occur at the farthest point of the orbit.

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