We can solve this by using the Newton's Law of universal gravitation, according to which the force of gravity is directly proportional to the product of masses of the two bodies and is inversely proportional to the square of the distance between them.

or, `F = G (m_1m_2)/r^2`

In this case,...

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We can solve this by using the Newton's Law of universal gravitation, according to which the force of gravity is directly proportional to the product of masses of the two bodies and is inversely proportional to the square of the distance between them.

or, `F = G (m_1m_2)/r^2`

In this case, if m1 is the mass of the planet and m2 is the mass of the spacecraft and r is the distance between them, the gravitational force between the dwarf and spacecraft can be given as,

Fd = G m1m2/r^2

It is also given that in case of Pluto, spacecraft is at half the distance (i.e, r/2) and it experiences half gravitational force from Dwarf planet as compared to Pluto, i.e. Fp = 2Fd

and assuming mass of pluto as mp, we get

Fg = Gmpm2/(r/2)^2 = 4 Gmpm2/r^2 = 2Fd = 2 Gm1m2/(r^2)

or, m1 = 2 mp

i.e. the dwarf planet has **2 times the mass of Pluto**.

Hope this helps.