PHYSICS MIDDLE SCHOOL

A spy satellite is orbiting earth and experiences a gravitation Force F if a similar satellite with one half the mass is placed in an orbit that is twice as far from the earths center the gravitational force between the earth and the second satellite will be what multiple of F?

Answers

Answer 1
Answer:

The gravitational force on the second satellite is 1/8 of the force exerted on the 1st satellite.

Explanation:

The magnitude of the gravitational force exerted by the Earth on the satellite is given by:

F=G(Mm)/(r^2)

where

G is the gravitational constant

M is the Earth's mass

m is the mass of the satellite

r is the radius of the orbit of the satellite

Let's call F the gravitational force on the first satellite, of mass m, with an orbit of radius r.

The second satellite has mass

m'=(m)/(2)

and the radius of its orbit is

r'=2r

So, the gravitational force exerted on the second satellite is

F'=G(M((m)/(2)))/((2r)^2)=(1)/(8)((GMm)/(r^2))=(1)/(8)F

Therefore, the force on the second satellite is 1/8 of the force exerted on the 1st satellite.

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Answers

Final answer:

To find the planet's radius in terms of the radius Rg of Earth, use the equation g = GM/R^2 and substitute 2g for g. Solve for R to get R = sqrt(1/(2gMg)) * Rg.

Explanation:

To find the planet's radius in terms of the radius Rg of Earth, we need to understand the relationship between the gravitational field and the mass and radius of a planet. The magnitude of the gravitational field on the surface of a planet is given by g = GM/R2, where G is the gravitational constant, M is the mass of the planet, and R is its radius. For the planet in question, we are told that the magnitude of the gravitational field is 2g and its mass is half the mass of Earth. Since the gravitational field is 2g, we can substitute g with 2g in the equation and solve for R in terms of Rg:

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Explanation:

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