# Question:Physics & Math with maple (DE numerically)

## Question:Physics & Math with maple (DE numerically)

Maple 2017

This is my first time in this forum, so I hope I use the correct conventions. If not please notice me.

1. When a light body orbits a heavy body under the influence of gravity (e.g. a planet around the Sun), Newton’s laws show that the orbit is restricted to a two-dimensional plane and is given by the differential equation

d2/d(φ)2(1/r(φ)) + 1/r(φ) = GM/h2

Here, (r, φ) is the path of the light body in polar coordinates, M is the mass of the heavy body, G is the gravitational constant, and h is a constant related to the angular velocity of the light body (h = r2φ ̇). The heavy body can be considered to be approximately stationary and located at the origin.

Use Maple to solve this differential equation numerically, taking M = 1, G = 1, h = 1 with initial conditions

r(0)=2/3, r′(0)=dr/dφ (0) = 0

Using polar coordinates, create a plot of the orbit (r(φ), φ) for
0 ≤ φ < 2π. You should observe a perfect ellipse.

2. Since I am not a frequent maple user, I hope somebody can help me here

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