Two isolated masses attract gravitationally. What direction is the force on each mass?

One mass is doubled, the other is tripled, and their separation is quadrupled. By what factor does the gravitational force magnitude change?

Using \(G=6.67\times10^{-11}\,\mathrm{N\,m^2\,kg^{-2}}\), find the gravitational force magnitude between \(6.0\,\mathrm{kg}\) and \(9.0\,\mathrm{kg}\) masses separated by \(0.30\,\mathrm{m}\).

Outside a spherical body of mass \(4.5\times10^{24}\,\mathrm{kg}\), find the gravitational field magnitude at \(r=9.0\times10^6\,\mathrm{m}\) from its center.

A test mass \(m\) is at \(x=a\), and a source mass \(M\) is at the origin. Write the vector gravitational force on \(m\) using \(\hat{\imath}\).

A probe moves from radius \(R\) to radius \(3R\) around the same spherical source. What happens to the gravitational field magnitude and to the probe's weight?

Around a body of mass \(5.0\times10^{24}\,\mathrm{kg}\), at what radius is the gravitational field magnitude \(1.5\,\mathrm{N\,kg^{-1}}\)? Use \(G=6.67\times10^{-11}\,\mathrm{N\,m^2\,kg^{-2}}\).

Two equal masses are fixed at \(x=0\) and \(x=d\). Where on the line between them is the net gravitational field zero, and why is it not zero outside the interval?

Mass \(M\) is fixed at \(x=0\), and mass \(9M\) is fixed at \(x=d\). Find the point between them where the net gravitational field is zero.

Two spherical source masses \(M_A\) and \(M_B\) are separated by distance \(d\). Derive the location of the zero-field point between them, measured from \(M_A\), and interpret which source it lies closer to.