1. A planet with a mass of 7.5 x 1025 kg moves around a 9.5 x 1031 kg star in a perfectly circular orbit with a radius of 9.3 x 107 km. The universal gravitational constant is G = 6.67 x 1011 m3 kg' s2. a. What is the magnitude of the force of gravity that the star exerts on the planet?10. b. What is the speed of the planet's orbit around the star, in units of km/s? c. What is the period of the planet's orbit around the star, in Earth days?

A satellite of mass 200 kg is launched from a site on Earth’s equator into an orbit 200 km above the surface of Earth. a. What is the satellite’s speed before it’s launched (in m/s)? (Hopefully, it’s moving along with the surface of the Earth as the Earth rotates.) b. What is the satellite’s speed in its orbit (in m/s)? (Remember there is only onespeed a satellite can have in order to maintain a stable circular orbit with agiven radius.) c. Assuming a circular orbit, what is the orbital period of this satellite? (In other words, how long (in hours) does it take for the satellite to complete one orbit?) d. What is the minimum energy (work) necessary to place the satellite in orbit,assuming no air friction? (Remember, work is the amount of energy added tothe system, and the total energy of the system is a combination of kinetic andgravitational potential energies.)

Two planets orbit a star. You can ignore the gravitational interactions between the planets. Planet 1 has orbital radius r₁, and planet 2 has r₂ = 4r₁ Planet 1 orbits with period T₁ Planet 2 orbits with period A. T₂ = -1/T₁ B. T₂=2T₁ C. T₂ = 4T₁ D. T₂=8T₁

2. a. Consider two planets orbiting a distant star. Planet A is further from the star. A is orbiting at a speed of 14625 m/s and has an orbital period of 12.45 years. What is the radius of A's orbit? Hint: remember to convert the period into seconds. 4.57E11 Previous submissions: 457000000000 b. What is the mass of the star? 1.465E30 Previous submissions: 1.465e30 kg c. Planet B is closer in. B has a larger velocity of 38500 m/s. What is the radius of B's orbit? 6.598E10 Previous submissions: m 65980000000 m m kg m incorrect incorrect V incorrect

1. Gravity: A satellite circles the earth three times per day (it has an 8-hour period). Given Mearth = 5.98x1024 kg, rearth = 6.38x10° km, and G=6.67x10" Nm²/kg², and assuming the orbit is circular, a. Find the radius of the orbit, how many earth radii is it? b. What is the speed of the satellite (in km/s)? c. What is the acceleration due to the Earth's gravity at that radius, i.e. what is "g" at the satellite radius? How much stronger is g at the Earth's surface (what is g/g.t_sat)?

4. Astronomers use a telescope to watch a small moon orbit a planet in our solar system. They find that it takes the moon 14 days to go around the planet once, and they estimate the radius of the moon's orbit is about 4.2 x 10² meters. a. From this information, estimate the mass of the planet. b. Using the mass you found in part (a), estimate the free-fall acceleration on the planet's surface if it has a radius of 3.8 x 106 meters.

1. Determine the force of gravitational attraction between a 67-kg father and his 12.8-kg son if they are separated at a distance of 5.29 x 105 m from each other. a. 1.02 x 1029 N b. 1.44 x 10-5 N c. 1.01 x 10-7 N d. 2.04 x 10-19 N 2. Two objects with equal masses of 1 kg each are separated by a distance of 1 m. The gravitational force between the objects is: a. Slightly less than G b. Slightly greater than G c. Equal to G d. Half as much as G