Mars has a mass of 6.419 times 10^23 kg, a radius of 3.397 times 10^6 m and a ro

Question

Mars has a mass of 6.419 times 10^23 kg, a radius of 3.397 times 10^6 m and a rotational period (length of day) of 24hrs 37m 22s. Find the orbital radius and altitude of a synchronous communication satellite orbiting Mars. 2) The Martian year is 1.881 Earth years. What is Mars' distance from the Sun? 3) a) What is the ratio of the Sun's gravitational force on the Earth to the Moon's force? b) What is the ratio of the Moon's gravitational force to the Earth's force on the 79,135 kg Space Shuttle Orbiter Atlantis when it is in orbit (167.0 km above Earth's surface). 4) A 910,000 kg asteroid and a 41,000 kg spacecraft are 200 m apart. There are no other bodies nearby. Find the acceleration of the asteroid and the spacecraft, and their velocities after 8.00 s. 5) A car of mass m goes around an unbanked curve of radius 30.0 m at a velocity of 25 m/s. Is it possible for the car to stay on the roadway? 6) A ball traveling at 2.00 m/s strikes a wall, exerting a force on the wall of 25.0 N. The ball's mass is 0.35kg. The ball is in contact with the wall for 0.050 s. What is the ball's displacement 4.00 s after hitting the wall? 7) The Saturn V rocket (used to launch Apollo spacecraft) has a mass of 5.4 times 10^2 kg. The first stage booster has five engines which each deliver a thrust of 1.48 times 10^6 N. Neglecting mass loss. what is the acceleration of the rocket? 8) An amusement park ride called The Swing consists of a chair hanging from a 4.5 m long chain. The top of the chain is attached to a rotating spindle. When the ride is in motion, the chair moves in a horizontal circle and the chain makes an angle of 25.0degree with the vertical (see diagram). If a rider experiences a radial acceleration of 3g what is the ride's period? 9) In the diagram at right, M_1 = 5.55 kg, M_2 = 2.33 kg. A) What is the minimum coefficient of static friction mu such that the system is in equilibrium? B) What is the maximum value for M_2 so that equilibrium is still possible? 10) A car of mass M goes around an unbanked curve of radius R. Find the maximum velocity the car can have and still May on the road. 11) In the diagram at right, a mass M = 17.5 kg is hanging from two cables as shown. Find the tension in cach cable. theta = 35.0degree, = 44.0degree 12) A 1.75 kg ball is attached to 2 identical rubber bands, as shown. The rubber bands are attached to a wall. When you let go of the ball, it will sag down. What angle will the rubber bands make with the horizontal? (Find in terms of T, the tension in each rubber band)

Explanation / Answer

These are seperate questions i can only answer one among these please repost to get othere.

We know that the time period of a planet

GM = 2*pi*R^2/T

T is proportional to R^2

So

Te/Tm = Re^2/ Rm^2

1/1.881 = Re^2/ Rm^2

Rm = Re*1.37

Hence the radius of mars's orbit is 1.37 time that of earth

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