Question

1.) The Hubble Space Telescope orbits the Earth at an approximate altitude of 612 km. Its mass is 11,100 kg and the mass of the Earth is 5.97×1024 kg. The Earth's average radius is 6.38×106 m. What is the magnitude of the gravitational force that the Earth exerts on the Hubble? (Answer in N)

2.) A planetoid has a mass of 2.310e+21 kg and a radius of 7.00×105 m. Find the magnitude of the gravitational acceleration at the planetoid's surface. (Answer in m/s^2) 3. An asteroid orbiting the Sun has a mass of 4.00×1016 kg. At a particular instant, it experiences a gravitational force of 3.14×1013 N from the Sun. The mass of the Sun is 1.99×1030 kg. How far is the asteroid from the Sun? ( Answer in m )

Answer 1

1)

From Universal law of gravitation, the magnitude of the gravitational force that the Earth exerts on the Hubble Space Telescope is

Here, gravitational constant is G, mass of the Earth is M_E, Mass of the Hubble Space Telescope is M_H, radius of the Earth is R and distance between the Earth and the Hubble space telescope is r.

Substitute 6.67 x 10-11 Nm² /kg² for G, 5.97×10²⁴ kg for M_E, 11,100 kg for M_H, 612 km for r and 6.38×10⁶ m for R in the above equation,

Rounding off to three significant figures, the magnitude of the gravitational force that the Earth exerts on the Hubble Space Telescope is 9.04 x 10⁴ N.

2)

The magnitude of the gravitational acceleration at the surface of the planetoid is

Here, mass of the asteroid is M_P and radius of the asteroid is R_P.

Substitute 6.67 x 10^-11 Nm² /kg² for G, 2.31×10²¹ kg for M_P and 7.00×10⁵ m for R_P in the above equation,

Rounding off to three significant figures, the magnitude of the gravitational acceleration at the surface of the planetoid is 0.314 m/s².

3)

The magnitude of the gravitational force between the Sun and the asteroid is

Here, mass of the Sun is M_S, mass of the asteroid is M_A and distance of the asteroid from the center of the Sun is r_A.

From the above equation,

Substitute 6.67 x 10^-11 Nm² /kg² for G, 1.99×10³⁰ kg for M_S , 4.00×1016 kg for M_A and 3.14×10¹³ N for F_SA in the above equation,

Rounding off to three significant figures, the asteroid is at a distance 4.11 x 10¹¹ m from the center of the Sun.