I need to calculate the average orbital speed Ceres in miles per hour when it is closest to the sun and when it is farthest away

Answer 1

If you look up Ceres statistics, the following information is available:

Aphelion (r_a) = 445,410,000,000 m

Perihelion (r_o) = 382,620,000,000 m

Eccentricity (e) = .075823

G (Gravitational Constant) = 6.674 x 10^-11 m³/(Kg-sec²)

Mass of Sun (M) = 1.9891 x 10³⁰ Kg

Let r_o = radius of Ceres orbit when it is closest to the sun

v_o = velocity of Ceres orbit when it is closest to the sun

w_a = angular velocity at the Aphelion

v_a = velocity of Ceres at the Aphelion

Then e + 1 = r_ov_o²/GM = 1.075823 = 2.88 x 10⁹ Solving for v_o = 19,320 m/sec

(r_a)²w_a= r_ov_o Solving for w_a = 3.726 x 10^-8/sec

then v_a = r_aw_a = (445,410 x 10⁶ m)(3.726 x 10^-8/sec) = 16,597 m/sec