You are given the initial positions and velocities and masses. Because the mass of the Sun...

       

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You are given the initial positions and velocities and masses. Because the mass of the Sun is so much bigger than those of Earth and Moon, we can consider the Sun fixed at the origin of our coordinate system and you only have to calculate the trajectories of Earth and Moon. The problem is broken down into four smaller zyLabs. Most of the background and theory is written down in this zyLab, though, and you can come back to this problem when you are working on later zyLabs. However, in this zyLab you will only have to calculate forces. You will then use your force calculations in subsequent zyLabs (copy & paste your own code). Newton's law of gravity The bodies interact via Newton's law of gravity. The force depends on the distance between the two bodies with an inverse square law and the masses of the bodies. Specifically, the force on body i at position r; due to body j at position r, is Gm,mj Fij = F(ri, rj) = F(rij) Tijri-rj rij fij rij rij= √Tij. Tij Tij The two bodies have masses m, and m; and G is the gravitational constant. The vector is the unit vector pointing from body j towards body. The scalar r is the length of the difference vector i and rijri = r2, is the inner product (or dot product, see below) of the vector with itself. For example, if we want to calculate the force on the Earth E due to the Sun S where rs = 0 = (0, 0, 0) (because the Sun is fixed at the origin) we get FES(TE) Lfij GmEms -TE, You are given the initial positions and velocities and masses. Because the mass of the Sun is so much bigger than those of Earth and Moon, we can consider the Sun fixed at the origin of our coordinate system and you only have to calculate the trajectories of Earth and Moon. The problem is broken down into four smaller zyLabs. Most of the background and theory is written down in this zyLab, though, and you can come back to this problem when you are working on later zyLabs. However, in this zyLab you will only have to calculate forces. You will then use your force calculations in subsequent zyLabs (copy & paste your own code). Newton's law of gravity The bodies interact via Newton's law of gravity. The force depends on the distance between the two bodies with an inverse square law and the masses of the bodies. Specifically, the force on body i at position r; due to body j at position r, is Gm,mj Fij = F(ri, rj) = F(rij) Tijri-rj rij fij rij rij= √Tij. Tij Tij The two bodies have masses m, and m; and G is the gravitational constant. The vector is the unit vector pointing from body j towards body. The scalar r is the length of the difference vector i and rijri = r2, is the inner product (or dot product, see below) of the vector with itself. For example, if we want to calculate the force on the Earth E due to the Sun S where rs = 0 = (0, 0, 0) (because the Sun is fixed at the origin) we get FES(TE) Lfij GmEms -TE,