18. the gravitational acceleration at the surface of planet x is 11.6 m/s, and the radius of the planet is 66,500 km. an astronaut is hovering at
height h above the planet's surface, and she notices her weight is the same as it is on earth. what is h?
7000 km
8200 km
5800 km
9400 km

Based on the information given, the value of the height will be 5800 km.

The gravitational force will be given as:

g = GM/r²

where,

Solving for r₂ will be equal to

r₂ = r₁ √(g₁ / g₂)

It should be noted that when r = 66,500 km, g = 11.6 m/s².

Also, when r = h + 66,500 km, g = 9.8 m/s².

Therefore,

h + 66,500 km = 66,500 km × √(11.6 / 9.8)

h + 66,500 km = 72,300 km

Collect like terms

h = 72300km - 66500km

h = 5800 km

In conclusion, the height is 5800km.

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5800 km

Explanation:

Gravitational acceleration is:

g = GM / r²

where G is gravitational constant,

M is the mass of the planet,

and r is the distance from the center.

G and M are constant, so:

g₁ r₁² = g₂ r₂²

Solving for r₂:

r₂ = r₁ √(g₁ / g₂)

When r = 66,500 km, g = 11.6 m/s².

When r = h + 66,500 km, g = 9.8 m/s².

h + 66,500 km = 66,500 km √(11.6 m/s² / 9.8 m/s²)

h + 66,500 km = 72,300 km

h = 5800 km

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