Question

Two planetoids with radii R1 and R2 and local accelerations g1 and g2 are separated by a centre-to-centre distance D, and are members of a simple two-body system. A rocket is located on planetoid 1 and is scheduled to launch from this planetoid to a point between the planetoids where the net gravitational force on the rocket by the two planetoids is zero. At what distance from the centre of planetoid 1 is the zero gravitational point? Choose R1 = 1400m, R2 = 1000m, g1 = 7.5m/s2, g2 = 5.3m/s2 and D = 4800m. [5 points]

Answer 1

Answer:

Therefore, the gravitational zero points between two planetoids lie at a distance of 3000 m from the center of planetoid 1.

Explanation:

From Newton’s gravitation formula, the expression of the mass (M) of the planet of radius R is given as,

$F_{G} = mg_{1}\\ \left ( \frac{GMm}{{R_{1}}^{2}} \right )=mg_{1}\\\\M= \frac{gR^{2}}{G}\rightarrow \left ( 1 \right )$

Let's take x to be the distance of the zero gravitational points from the center of the planetoid 1.

Thus, the distance of the zero gravitational points from the center of the planetoid 2 is (D-x).

At zero gravitational point, the gravitational force between the planets and the rocket must be equal.