Help Needed: Solving Kepler's Third Law for a Solar Elliptical Orbit

In summary, the problem involves calculating the number of days required for a space probe to travel from Earth to Venus using Kepler's third law and information about the orbits of Venus and Earth. The solution involves finding the semimajor axis of the elliptical orbit and using it to calculate the period of the orbit, which is equivalent to the number of days required for the space probe to reach Venus.
  • #1
nick227
36
0

Homework Statement



I have this problem for homework and I don't know how to even start. Can someone help? Thanks in advance.A neat and exploitive use of the sun would be to put a space probe into a solar elliptical orbit from the Earth on one side of the sun headed towards a rendezvous with Venus on the other side. Since Venus is a moving object, it would actually meet the space probe at the other end of the ellipse. So, employing Kepler's third law determine how many days are required for the space probe to travel to Venus. Consider both Venus and the Earth to have circular orbits. Also use this information:
Period(yr) Radius(AU) Eccentricity

Venus .615 .723 .007
Earth 1.000 1.000 .017

Homework Equations



t^2=((4pi^2)/(GM))a^3
t =period
G=universal gravity
M=mass of sun...?
a=semimajor axis or radius for a circle

The Attempt at a Solution



i don't really know how to start this. can anyone get me started?
 
Physics news on Phys.org
  • #2
The farthest point from the sun in the orbit is at the radius of the Earth's orbit. The closest is at the radius of Venus' orbit on the opposite side of the sun from the first point. Draw a picture. You can use that info to find the semimajor axis of the ellipse since the distance between those two points is twice the semimajor axis.
 
  • #3
so...
1.723=2a
a=.8615

t=(.8615)^(3/2)=.800yr

.800*365 = 292 days

292 is the answer. thanks a lot.
 

What is Kepler's Third Law?

Kepler's Third Law, also known as the harmonic law, states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. In simpler terms, it relates the time it takes for a planet to orbit the sun to its distance from the sun.

Why is it important to solve Kepler's Third Law for a Solar Elliptical Orbit?

Solving Kepler's Third Law for a Solar Elliptical Orbit is important because it allows us to accurately predict the orbital periods and distances of planets in our solar system, as well as in other solar systems. This information is crucial for understanding the dynamics and stability of planetary systems, and for space exploration and navigation.

What are the main challenges in solving Kepler's Third Law for a Solar Elliptical Orbit?

The main challenges in solving Kepler's Third Law for a Solar Elliptical Orbit include accurately measuring the orbital period and semi-major axis of the planet, and accounting for any perturbations or deviations from a perfect elliptical orbit caused by other planets or external forces. Additionally, the use of complex mathematical equations and calculations is required to accurately solve the law.

What are some potential applications of solving Kepler's Third Law for a Solar Elliptical Orbit?

The applications of solving Kepler's Third Law for a Solar Elliptical Orbit are wide-ranging. They include predicting the positions and movements of planets for space missions, designing and optimizing satellite orbits, and studying the formation and evolution of planetary systems. Additionally, this law has been used to discover new exoplanets and to determine their properties.

Is there any ongoing research or advancements in solving Kepler's Third Law for a Solar Elliptical Orbit?

Yes, there is ongoing research and advancements in solving Kepler's Third Law for a Solar Elliptical Orbit. With the use of advanced technologies and techniques such as satellite observations and computer simulations, scientists continue to refine and improve our understanding of this law and its applications. Additionally, there is ongoing research to extend this law to other types of orbits, such as non-Euclidean and relativistic orbits.

Similar threads

Find the location knowing the resonance using Kepler's third law
    • Introductory Physics Homework Help
Replies
2
Views
426
Orbital Perturbations: Solving for Equations of Motion in Elliptical Orbits
    • Advanced Physics Homework Help
Replies
1
Views
1K
Kepler's Third Law vs Conservation of angular momentum
    • Introductory Physics Homework Help
Replies
8
Views
1K
Kepler's third law for elliptical orbits
    • Astronomy and Astrophysics
Replies
10
Views
5K
Third kepler's law error on sun mass calculation
    • Advanced Physics Homework Help
Replies
1
Views
3K
Apparent (clearly false) contradiction - Kepler's Third Law
    • Introductory Physics Homework Help
Replies
2
Views
965
I with understanding Kepler's second law
    • Thermodynamics
Replies
9
Views
1K
Using Kepler's 3rd Law to find Period of Venus
    • Introductory Physics Homework Help
Replies
4
Views
2K
Kepler's law of periods problems about orbiting satellite
    • Introductory Physics Homework Help
Replies
7
Views
3K
Using Kepler's Third Law to find mass
    • Calculus and Beyond Homework Help
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top