For the angle of the throw you mentioned **70 degrees**. Is this from the vertical or the horizontal? This can impact the answer. I will be using from the horizontal in this example. I am also assuming that from the throwers point of view that the **surface is approximately flat**.

To begin, we must convert the data into **SI** units to make sure the units are consistent.

- The density in the SI units would be kg/m^3 so 4.6 g/cm^3 would become **4,600 kg/m^3**.
- The radius in SI units would be in meters so it would become **4,600,000 meters**.
- The velocity is already in SI units so no change needed, **400 m/s**.

To get the mass of the planet we use the equation **m = d*V** where m is the mass, V is the volume and d is the density.
To get the Volume of the planet we use the equation **V = (4/3)*pi*r^3**

- The volume of the planet is therefore **4.0772 * 10 ^ 20**
- This means the mass of the planet is **1.8755 * 10 ^24**

We now need to use Newtons equation for gravity **G m1*m2/r^2 = m1*g**. Here m1 is the mass of the thrown object and m2 is the mass of the planet. We want to solve for **g** the acceleration due to gravity at the surface of the planet. Solving for g gives **g = G*m2/r^2**. Remember G is the gravitational constant of 6.674 * 10 ^ -11

- We plug this in to obtain the acceleration of **5.815 m/s^2**

Now we move on to simple kinematics. We can model the **x** and **y** components of the object as a function of time

- The x-component would be modeled by **x = v_x * t**
- The y-component would be modeled by **y = -(1/2) * g * t^2+v_y * t**

Here v_x and v_y represent the initial velocity in each component. 

- v_x = cos(70)*400
- v_y = sin(70)*400

^ (this part changes if you meant from the vertical)

Solving the quadratic equation from the y-component we can find that the ball reaches the ground after **127.082 seconds**. We can use this to find the maximum horizontal displacement to be
- **x_max = 17,386 meters**.

The vertex of this parabola has a maximum height of 
- **y_max = 11,941 meters**.

There are a lot of steps involved in this problem, If you need any further clarifications, let me know!
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