his a question on Cosmology: Suppose that you have a flat universe that has matter and dark energy with wd = -2/3 & Ωd,0 =0.7 At the time when light with z = 1 was emitted from a distant galaxy what was the ratio Ɛd /Ɛm ?

A 50 g tennis ball revolves around a 2-kg bowling ball in a universe that is otherwise empty. If the orbit is circular with radius of 10 m, calculate: a) The speed of the tennis ball b) The period of its motion Take the tennis ball and the bowling ball as particles.

Suppose the energy density of the cosmological constant is equal to the present critical density, 8.7 x 10-27 kg m-3 \times ×c2. What is the total energy of the cosmological constant within a sphere 1.00 AU in radius? Input answer in units of Joules, and must be in scientific notation and include one decimal places (2 sig fig).

Consider a US Air Force launch of its latest GPS satellite from Cape Canaveral.  Radar tracking shows the following J2000 state vector (X,Y,Z and Vx,Vy,Vz) at burnout.   26 Feb 2022 17:10:00.000    (X,Y,Z): 5210.345121    -549.481941    4300.883291       (Vx,Vy,Vz): -1.451280      7.391098     2.690198   Calculate the minimum total delta V required to maneuver this spacecraft into a circular orbit with a 12-hour period and an inclination of 61 degrees, assuming impulsive maneuvers and two-body dynamics.   Please solve using equations from Howard Curtis's Orbital Mechanics for Engineering Students, 4th Edition. Or if not possible name the equations you use. Also please use matlab syntax for solving or write the equations out clearly. Thanks!