010: A new planet (tentatively named “Melmac") is found in a circular orbit with a period of 571 years. The sun has a mass of 1.9891x1030 kg. How far away is the planet in Astronomical Units (AU) ? Note: An A.U. is 1.496x1011 m.

Earth Mars Saturn answers, include units 1 AU=1.496 x 10" m and Mun= 1.989 x 10 kg Mass of planet Radius of (kg) planet (km) 6371.0 3389.5 58,232 5.972x1024 6.417x102 5.683x102 Semimajor axis Eccentricity of Period of orbit of orbit a (AU) orbit e T (years) 1.00 0.0167 1.00 0.0934 1.88 0.0565 9.58 a) Use Kepler's 3rd Law to find the semimajor axis of Mars' orbit. AU m b) Use Kepler's 3rd Law to find the period of Saturn's orbit. c) Find the gravitational acceleration on the surface of Mars both in m/s² and as a multiple of Earth's gravitational acceleration. yrs m/s² g For (d) and (e), Earth's orbit is elliptical (ez0) but the semimajor axis is the average radius of the orbit so using the semimajor axis as the radius will let you solve for the average force and speed. d) Find the average force of gravity on the Earth from the Sun. e) Find the average speed of Earth as it moves around its orbit. N m/s

2. The mean distance between the earth and the sun is 1.5 x 1011m. The mean distance between the sun and Venus is 1.08 x 108km. What is the period of Venus around the sun in earth- days?

3. The gravitational acceleration at Earth's surface (ga) is about 10 m/s? and ge = GM/R2. What is g, at the surface of a planet with 2X Earth's mass and 3X Earth's radius?

An intergalactic spaceship arrives at a distant planet that rotates on its axis with a period of T = 31 hours. The mass of the planet is M = 2.1 • 1025 kg. The spaceship enters a circular orbit with an orbital period that is equal to the planet's period for the rotation about its axis, T.   a.  Enter an expression for the radius of the spaceship’s orbit.  b.  Calculate the orbital radius in meters.

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

2. An unknown planet was accidentally discovered by NASA. It has a mean distance of 2.15 E11 meters from the sun. Assuming it has a mass of 6.02 E24 kg, how long (in Earth Years) will it take for the said planet to revolve around the sun?

The moon on Mars Phobos ( Fear) and Deimos ( Terror) are very close to the planet compared to Earth's Moon. Their orbital radii are 9,376 km and 23,463.2 km respectively. A) what is the orbital speed of Phobos to that of Deimos? B) If the period of Phobos orbits 7hr 39.2 min, what is the mass of Mars? C) Calculate the orbital period of Deimos.

Scientists have discovered a distant planet with a mass of 8.2x1023 kg. The planet has a small moon that orbits with a period of 6 hours and 36 minutes. Use only this information (and the value of G) to calculate the radius of the moon's orbit (in units of 106 m).