A space agency is planning to launch a spacecraft from the equator of Mars. Given that Mars has a rotational speed of 0.98 rev/day, determine the escape velocity required in order for the spacecraft to lift off and to exit Mars's gravitational pull. [Hint: The mass and the radius of Mars are 6.4 × 10²³ kg and 3.4 × 10⁶ m respectively. Note that rotational speed of 0.98 rev/day, is equivalent to one Earth day rotation.]

An asteroid in our solar system has a radius of about 7 × 10⁶ m and an escape velocity from its surface is 12 × 10³ m/s. What would be its gravitational pull?

A private space company plans to mine an asteroid in the near future. The asteroid being considered for mining has a mass of about 3 × 10¹⁷ kg and a diameter of around 15 km. What would be the required speed to leave its surface?