Calculate the position of the center of mass of the following pairs of objects. Use a
coordinate system where the origin is at the center of the more massive object. Give your
answer not in meters but as a fraction of the radius as requested. Get data from inside
the front cover of your text.
(a) The Earth and the Moon. Give the answer as a fraction of the earth's radius.
(b) The Sun and the Earth. Give the answer as a fraction of the sun's radius.
(c) The Sun and Jupiter. Give the answer as a fraction of the sun's radius.
I got a) 1.36, b) 1.55e3 c) .938 all are incorrect please help
To calculate the position of the center of mass, we need to know the masses and distances of the objects involved. The data required for the calculations can be found on the inside cover of your textbook.
(a) The Earth and the Moon:
Let's denote the mass of the Earth as M_Earth and the mass of the Moon as M_Moon. The radius of the Earth is denoted as R_Earth.
The center of mass position, denoted as X_CoM, is given by the formula:
X_CoM = (m1 * x1 + m2 * x2) / (m1 + m2),
where m1 and m2 are the masses of the objects, and x1 and x2 are their respective positions.
In this case, the Earth is more massive than the Moon. Since we are using a coordinate system where the origin is at the center of the Earth, the position of the Earth is 0, and the position of the Moon is the distance between the Earth and the Moon denoted as D_Moon.
X_CoM = (M_Earth * 0 + M_Moon * D_Moon) / (M_Earth + M_Moon)
To express the answer as a fraction of the Earth's radius, we divide the position of the center of mass by the radius of the Earth, R_Earth:
X_CoM_Ratio = X_CoM / R_Earth = (M_Earth * 0 + M_Moon * D_Moon) / (M_Earth + M_Moon * R_Earth)
(b) The Sun and the Earth:
Let's denote the mass of the Sun as M_Sun and the distance between the Sun and Earth as D_Earth. The radius of the Sun is denoted as R_Sun.
Since the Sun is more massive than the Earth, our coordinate system origin is at the center of the Sun, making the position of the Sun 0, and the position of the Earth is D_Earth.
X_CoM = (M_Sun * 0 + M_Earth * D_Earth) / (M_Sun + M_Earth)
To express the answer as a fraction of the Sun's radius, we divide the position of the center of mass by the radius of the Sun, R_Sun:
X_CoM_Ratio = X_CoM / R_Sun = (M_Sun * 0 + M_Earth * D_Earth) / (M_Sun + M_Earth * R_Sun)
(c) The Sun and Jupiter:
Let's denote the mass of Jupiter as M_Jupiter and the distance between the Sun and Jupiter as D_Jupiter.
Similarly, using the same coordinate system, the position of the Sun is 0, and the position of Jupiter is D_Jupiter.
X_CoM = (M_Sun * 0 + M_Jupiter * D_Jupiter) / (M_Sun + M_Jupiter)
To express the answer as a fraction of the Sun's radius, we divide the position of the center of mass by the radius of the Sun, R_Sun:
X_CoM_Ratio = X_CoM / R_Sun = (M_Sun * 0 + M_Jupiter * D_Jupiter) / (M_Sun + M_Jupiter * R_Sun)