What is the weight of the Earth?

How high does a rocket have to go above Earth's surface before its weight is half of what it is on Earth?

• How high does a rocket have to go above Earth's surface before its weight is half of what it is on Earth? How can I solve this?

• Answer:

  Weiht is the force of mass pulled by gravity, and gravoty decreases by the square of the distance from the center of the Earth (or any other large body). At 1 Earth radius above the Earth (2 from the center), you would weigh 1/4 of what you weigh on the surface (1 Earth radius). Formula: g = 1/d^2, where g is the acceleration due to gravity from which weight is determined, and d is the distance from the center of the attracting body. To find the altitude where you would weigh 1/2 your surface weight, use 1/2 for g and solve for d: 0.5 = 1/d^2. d^2 = 1/0.5 d = sqr. root (1/0.5) d = sqr. root(2) Earth radius Earth radius = 3959 mi. = 6,371 km d = 5,598.9 mi. = 9,010.6 km (above Earth's center) distance above Earth's surface = 1,639.9 mi. = 2,639.1 km At this altitude, something will weigh half of what it would at Earth's surface.