Consider a planet of mass \(6 \times 10^{24} \textrm{kg}\) and radius
\(6 \times 10^3 \textrm{km}\). The density of air on this planet decays exponentially
with distance from the surface with the data \(f\left(0\textrm{m}\right)=2 \textrm{kg}/
\textrm{m}^3\) and \( f\left(3000\textrm{m}\right)=\frac{4}{3} \textrm{kg}/
\textrm{m}^3\). The planet has a moon with mass
\(7 \times 10^{22} \textrm{kg}\) and radius \(2 \times 10^3 \textrm{km}\). The moon
travels in perfectly circular orbit around the planet with an orbital distance between
the two centers of mass of \(4 \times 10^5 \textrm{km}\). On this moon there is a
life time supply of sweet, sweet, moon cheddar. You want to fire a rocket at the moon.
The day you plan to launch the moon will be directly over head. On the x-y plane put the
center of mass at the point \(\left(0, 4 \times 10^5 \textrm{km}\right)\) when
\(t=0 \textrm{s}\). Your space ship and you have a mass of \(1000 \textrm{kg}\) and the
rockets give a force of \(3 \times 10^3 \textrm{N}\) for \(500 \textrm{s}\). Your rocket
has a coefficient of drag of \(C_d = 1.33\) and its cross sectional area is
\(5.00 \textrm{m}^2\). Find an from the normal vector of the planet such that you hit the
moon. (5 points) If you can try to travel around the darkside of the moon, without
hitting it and return to your home planet. (7 points) INCLUDE FRICTION! Submit your
code, a graph of the moon's path and the rockets path, and your calculations with an
explanation.
Alright let's try to solve this problem with numbers!
This is what a blank numbers document looks like. It's good to put your constants in their own cells. To get a cell to put in numerical numbers you can use the black "123" button to put in numbers and the black "=" button to put in equations.
Once you get everything ready you need to input the equation for acceleration. All accelerations should be from equations. Your initial position and velocity should be numbers from the problem.
The components of position and can be updated using the constant acceleration equations.
The components of velocity and can also be updated using the constant acceleration equations.
You can autofill the cells below your equation. Tap on the cell with the keyboard hidden and click on the option "Cell Actions". Then click on "Autofill Cells". This will let you autofill the cells.
Here's the cell I used to plot the surface of the Earth.
Here's my graph. You can make a graph by clicking on the "+" and navigating to the graph button.
JavaScript Link
Here's my graph using javascript and Chart.js.