##a=4.0″AU”##,
##e = .5##,
##T=2″years”##
The semi-major axis, ##a## of and ellipse is half of the major axis, the total distance between perihelion and aphelion. The semi-major axis is therefore equal to;
##a = (R_a + R_p)/2 = (6.0″AU”+2.0″AU”)/2 = 4.0″AU”##
Eccentricity is defined as the ratio of the distance between two focus of the ellipse, ##R_a – R_p##, and the length of the major axis, ##R_a + R_p##. This can be expressed mathematically as;
##e = (R_a – R_p)/(R_a + R_p) = (6.0″AU” – 2.0″AU”)/(6.0″AU”+2.0″AU”)=.5##
The period, ##T##, can be found using the Kepler’s 3rd law, which states that the ratio of the period squared to the semi-major axis cubed is a constant for all objects orbiting the same body. In other words, for two objects that orbit ;
##T_1^2/a_1^3 = T_2^2/a_2^3 = C##
Or, restated;
##T_1^2 = a_1^3/a_2^3 T_2^2##
If we use the Earth as object ##2##, then ##T_2## and ##a_2## are both ##1##. We can calculate the period of the asteroid using its semi-major axis, ##a=4.0″AU”##.
##T_1^2 = (4.0″AU”)^3/(1″AU”)^3 (1″year”)^2 = 4.0″years”^2##
Taking the square root, we get a period of ##2″years”## for the asteroid.
Our website has a team of professional writers who can help you write any of your homework. They will write your papers from scratch. We also have a team of editors just to make sure all papers are of HIGH QUALITY & PLAGIARISM FREE. To make an Order you only need to click Ask A Question and we will direct you to our Order Page at WriteDemy. Then fill Our Order Form with all your assignment instructions. Select your deadline and pay for your paper. You will get it few hours before your set deadline.
Fill in all the assignment paper details that are required in the order form with the standard information being the page count, deadline, academic level and type of paper. It is advisable to have this information at hand so that you can quickly fill in the necessary information needed in the form for the essay writer to be immediately assigned to your writing project. Make payment for the custom essay order to enable us to assign a suitable writer to your order. Payments are made through Paypal on a secured billing page. Finally, sit back and relax.
About Writedemy
We are a professional paper writing website. If you have searched a question and bumped into our website just know you are in the right place to get help in your coursework. We offer HIGH QUALITY & PLAGIARISM FREE Papers.
How It Works
To make an Order you only need to click on “Place Order” and we will direct you to our Order Page. Fill Our Order Form with all your assignment instructions. Select your deadline and pay for your paper. You will get it few hours before your set deadline.
Are there Discounts?
All new clients are eligible for 20% off in their first Order. Our payment method is safe and secure.