Can anyone help me ask these physics questions?

Question

A hypothetical planet has a radius 1.7 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surface?

What is the distance from the Earth's center to a point outside the Earth where the gravitational acceleration due to the Earth is 1/20 of its value at the Earth's surface?

Suppose the space shuttle is in orbit 410 km from the Earth's surface, and circles the Earth about once every 92.8 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g, the gravitational acceleration at the Earth's surface.

Thank you

Answer 1

Gravitational acceleration at the surface of a planet is directly proportional to the mass of the planet and inversely proportional to the square of the planet's radius. If the planet has the same mass as Earth, then the gravitational acceleration at the surface, 1.7 times further from the center than the surface of the Earth would be, is simply 1 / 1.7^2 times the acceleration at the surface of the Earth. That is, (1 / 1.7^2)g, where g is 9.8 m/s^2.

Using the same inverse square law, the gravitational acceleration decreases to 1/20 of that at the surface of the Earth when one's distance from the center of the Earth is R*sqrt(1/20), where R is the radius of the Earth.

Use the formula a = rw^2, r is radius and w is angular velocity. You can find the radius r by adding 410 km to R, the radius of the Earth. You can find w by converting (1 revolution / 92.8 minutes) into radians per second. Finally, divide your answer by 9.8 m/s^2 to get it in terms of g.